Finite Group Databasebeta

← #11772627

Subgroups — #11772627

Order 1152.

486 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C32×#408C211yesmaximal, characteristic
2#10592939C211yesmaximal, characteristic
3#10592936C211yesmaximal, characteristic
4#67692—34nomaximal
5C2×C32×#41C2211yescharacteristic
6C2×C32×M16C411yescharacteristic, complemented
7C22×C32×C8C411yescharacteristic, complemented
8#64135—21no—
9C2×#3748—21no—
10C32×C22⋊C8—21no—
11C32×C22⋊C8—21no—
12#63663C412yescomplemented
13#63661—21no—
14#63661C412yes—
15#63660—21no—
16C3×#408D314yes—
17#5240—34no—
18#5237—34no—
19C32×#41—41no—
20C32×#41—41no—
21C2×C32×Q8C2×C411yescharacteristic
22C2×C32×D4C2×C411yescharacteristic
23C2×C32×D4D411yescharacteristic
24C2×C32×D4Q811yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4D411yescharacteristic
28C32×M16—41no—
29C2×C32×C8—21no—
30C2×C32×C8—21no—
31C2×C32×C8—41no—
32#3757—22no—
33C4⋊(C3⋊Dic3)—41no—
34C4×C3⋊Dic3—41no—
35#3748—22no—
36#3748—41no—
37C2×C3⋊(C3⋊C8)—41no—
38#1395—91noSylow
39C2×C3×#41C2×D314yes—
40C2×C3×M16Dic314yescomplemented
41C22×C3×C8Dic314yescomplemented
42#926—64no—
43C2×#208—64no—
44C3×C22⋊C8—24no—
45C3×C22⋊C8—24no—
46#836—38no—
47#834—38no—
48#834—64no—
49#833—64no—
50C23×C32C22⋊C411yescharacteristic
51C23×C32C4⋊C411yescharacteristic
52C23×C32C4⋊C411yescharacteristic
53C32×Q8—41no—
54C32×D4—41no—
55C32×D4—41no—
56C32×D4—41no—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4C4211yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C4⋊C411yescharacteristic
67C2×C3⋊Dic3—42no—
68C32×C8—41no—
69C32×C8—41no—
70C3⋊(C3⋊C8)—42no—
71#413—91no—
72#410—91no—
73#408C3⋊D311yescharacteristic
74C3×#41—44no—
75C3×#41—44no—
76C2×C3×Q8C4×D314yes—
77C2×C3×D4Dic614yes—
78C2×C3×D4C4×D314yes—
79C2×C3×D4D1214yes—
80C22×C3×C4C2×Dic314yes—
81C22×C3×C4#6714yes—
82C22×C3×C4#6714yes—
83C3×M16—44no—
84C2×C3×C8—24no—
85C2×C3×C8—24no—
86C2×C3×C8—44no—
87#217—68no—
88C4⋊Dic3—124no—
89C4×Dic3—124no—
90#208—68no—
91#208—124no—
92C2×C3⋊C8—124no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—41no—
97C22×C32—41no—
98C22×C32—41no—
99C22×C32#9511yescharacteristic
100C32×C4—21no—
101C32×C4—21no—
102C32×C4—21no—
103C32×C4#9911yescharacteristic
104C32×C4#9911yescharacteristic
105C3⋊Dic3—82no—
106C2×#41C2×C3⋊D311yescharacteristic
107C2×M16—181no—
108C2×M16C3⋊Dic311yescharacteristic, complemented
109C22×C8C3⋊Dic311yescharacteristic, complemented
110#117—181no—
111#101—92no—
112#100—181no—
113#99—92no—
114#99—181no—
115C22⋊C8—21no—
116C22⋊C8—21no—
117C23×C3Dic3⋊C414yes—
118C23×C3C4⋊Dic314yes—
119C23×C3(C2×D3)⋊C414yes—
120C3×Q8—44no—
121C3×D4—44no—
122C3×D4—44no—
123C3×D4—44no—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×C3×C4C4×Dic314yes—
131C2×C3×C4Dic3⋊C414yes—
132C2×C3×C4(C2×D3)⋊C414yes—
133C2×C3×C4#21714yes—
134C2×Dic3—128no—
135C3×C8—44no—
136C3×C8—44no—
137C3⋊C8—128no—
138C2×C32—21no—
139C2×C32—41no—
140C2×C32—41no—
141C2×C32—41no—
142C2×C32#34211yescharacteristic
143#41—41no—
144#41—41no—
145C2×Q8C4×C3⋊D311yescharacteristic
146C2×D4#63411yescharacteristic
147C2×D4C4×C3⋊D311yescharacteristic
148C2×D4C4⋊(C3⋊D3)11yescharacteristic
149C22×C4C2×C3⋊Dic311yescharacteristic
150C22×C4#63811yescharacteristic
151C22×C4#63811yescharacteristic
152M16—41no—
153M16—182no—
154M16—361no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8—361no—
159C4⋊C4—361no—
160C22⋊C4—182no—
161C42—361no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—24no—
165C22×C3—44no—
166C22×C3—44no—
167C22×C3—44no—
168C22×C3C3⋊#9514yes—
169C3×C4—24no—
170C3×C4—24no—
171C3×C4—24no—
172C3×C4#83414yes—
173C3×C4#83414yes—
174Dic3—248no—
175C32#139511yescharacteristic, complemented, Sylow
176C23#375011yescharacteristic
177C23C4⋊(C3⋊Dic3)11yescharacteristic
178C23#375211yescharacteristic
179Q8—41no—
180D4—41no—
181D4—41no—
182D4—41no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—362no—
190C2×C4C4×C3⋊Dic311yescharacteristic
191C2×C4#375011yescharacteristic
192C2×C4#375211yescharacteristic
193C2×C4#375711yescharacteristic
194C8—41no—
195C8—41no—
196C8—362no—
197C2×C3—24no—
198C2×C3—44no—
199C2×C3—44no—
200C2×C3—44no—
201C2×C3#452614yes—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22#6365811yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—722no—
213C4#6366111yescharacteristic
214C4#6366111yescharacteristic
215C3#6769214yescomplemented
216C2—21no—
217C2—41no—
218C2—41no—
219C2—41no—
220C2#1058939211yescharacteristic
subgroupG/H
centerC4#63661
commutatorC2×C32×C4C42
FrattiniC2×#41C2×C3⋊D3
FittingC32×#408C2
socleC2×C32#342
prime radical, cosocleC2×C32×#41C22
hypercenter#408C3⋊D3
hypocenterC32#1395
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
6. C2×C32×M16C4semidirect
7. C22×C32×C8C4semidirect
12. #63663C4semidirect
40. C2×C3×M16Dic3semidirect
41. C22×C3×C8Dic3semidirect
108. C2×M16C3⋊Dic3semidirect
109. C22×C8C3⋊Dic3semidirect
175. C32#1395semidirect
215. C3#67692semidirect

Maximal subgroups

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

subgroupindex
C32×#4082
#105929392
#105929362
#676923