Finite Group Databasebeta

← C2×#557⋊C9 #11919723

Subgroups — C2×#557⋊C9 #11919723

Order 1152.

501 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 133 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#557⋊C9C214yesmaximal, direct product factor
2C2×C4×Q8⋊C9C211yesmaximal, characteristic
3C2×C4×Q8⋊C9C212yesmaximal
4C2×C3×#557C311yesmaximal, characteristic
5C22×Q8⋊C9C2211yescharacteristic
6C2×C9×C4⋊C4—41nomaximal
7C4×Q8⋊C9C2212yes—
8C4×Q8⋊C9C2214yes—
9C3×#557—34no—
10C3×#557C2×C314yes—
11C2×C3×C4⋊Q8—31no—
12C2×C3×#125—32no—
13C2×C3×C4×Q8—31no—
14C2×C3×C4×Q8C2×C312yes—
15C2×C3×C4×Q8C2×C311yescharacteristic
16C22×C4×C9—41no—
17C22×C4×C9—42no—
18C2×Q8⋊C9Q812yescomplemented
19C2×Q8⋊C9C2311yescharacteristic
20C9×C4⋊C4—44no—
21C2×#557C911yescharacteristic, complemented, Sylow
22C22×C3×Q8—31no—
23C22×C3×Q8C22×C311yescharacteristic
24C3×C4⋊Q8—34no—
25C3×C4⋊Q8—34no—
26C3×#125—38no—
27C3×#125—38no—
28C3×C4×Q8—34no—
29C3×C4×Q8—34no—
30C3×C4×Q8—34no—
31C3×C4×Q8—32no—
32C3×C4×Q8C22×C314yes—
33C3×C4×Q8C22×C312yes—
34C2×C3×C4⋊C4—31no—
35C2×C3×C4⋊C4—32no—
36C2×C3×C4⋊C4—32no—
37C2×C3×C4⋊C4—32no—
38C2×C3×C4⋊C4A411yescharacteristic
39C2×C3×C42—32no—
40C2×C3×C42—31no—
41C23×C9—41no—
42C2×C4×C9—44no—
43C2×C4×C9—42no—
44C2×C4×C9—44no—
45C2×C4×C9—84no—
46Q8⋊C9C2×Q811yescharacteristic, complemented
47#557—34no—
48#557C2×C914yescomplemented
49C2×C4⋊Q8—31no—
50C2×#125—32no—
51C2×C4×Q8—31no—
52C2×C4×Q8C2×C912yes—
53C2×C4×Q8C2×C911yescharacteristic
54C2×C3×Q8—34no—
55C2×C3×Q8—31no—
56C2×C3×Q8—32no—
57C2×C3×Q8—64no—
58C2×C3×Q8C3×Q812yes—
59C2×C3×Q8C23×C311yescharacteristic
60C22×C3×C4—31no—
61C22×C3×C4—31no—
62C22×C3×C4—32no—
63C22×C3×C4C2×A412yes—
64C22×C3×C4C2×A411yescharacteristic
65C3×C4⋊C4—32no—
66C3×C4⋊C4—34no—
67C3×C4⋊C4—32no—
68C3×C4⋊C4—34no—
69C3×C4⋊C4—38no—
70C3×C4⋊C4—38no—
71C3×C4⋊C4C2×A414yes—
72C3×C42—34no—
73C3×C42—32no—
74C3×C42—34no—
75C3×C42—32no—
76C22×C9—42no—
77C22×C9—42no—
78C22×C9—42no—
79C22×C9—41no—
80C4×C9—44no—
81C4×C9—84no—
82C22×Q8—31no—
83C22×Q8C22×C911yescharacteristic
84C4⋊Q8—34no—
85C4⋊Q8—34no—
86#125—38no—
87#125—38no—
88C4×Q8—34no—
89C4×Q8—34no—
90C4×Q8—34no—
91C4×Q8—32no—
92C4×Q8C22×C914yes—
93C4×Q8C22×C912yes—
94C2×C4⋊C4—31no—
95C2×C4⋊C4—32no—
96C2×C4⋊C4—32no—
97C2×C4⋊C4—32no—
98C2×C4⋊C4C22⋊C911yescharacteristic
99C2×C42—32no—
100C2×C42—31no—
101C23×C3C22×A411yescharacteristic
102C3×Q8—32no—
103C3×Q8—31no—
104C3×Q8—32no—
105C3×Q8—68no—
106C3×Q8C2×C3×Q811yescharacteristic
107C2×C3×C4—24no—
108C2×C3×C4—32no—
109C2×C3×C4—32no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—32no—
113C2×C3×C4—34no—
114C2×C3×C4—64no—
115C2×C3×C4—62no—
116C2×C3×C4#41⋊C314yes—
117C2×C3×C4C22×A414yes—
118C2×C3×C4C22×A412yes—
119C2×C9—41no—
120C2×C9—41no—
121C2×C9—41no—
122C2×C9—44no—
123C2×Q8—34no—
124C2×Q8—31no—
125C2×Q8—32no—
126C2×Q8—64no—
127C2×Q8Q8×C912yes—
128C2×Q8C23×C911yescharacteristic
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—32no—
132C22×C4C2×C22⋊C912yes—
133C22×C4C2×C22⋊C911yescharacteristic
134C4⋊C4—32no—
135C4⋊C4—34no—
136C4⋊C4—32no—
137C4⋊C4—34no—
138C4⋊C4—38no—
139C4⋊C4—38no—
140C4⋊C4C2×C22⋊C914yes—
141C42—34no—
142C42—32no—
143C42—34no—
144C42—32no—
145C22×C3Q8×A412yes—
146C22×C3C2×#41⋊C312yes—
147C22×C32−1+4⋊C312yes—
148C22×C3C23×A411yescharacteristic
149C3×C4—24no—
150C3×C4—31no—
151C3×C4—32no—
152C3×C4—31no—
153C3×C4—64no—
154C3×C4—62no—
155C3×C4C2×#41⋊C314yes—
156C9—41noSylow
157C23C22×C22⋊C911yescharacteristic
158Q8—32no—
159Q8—31no—
160Q8—32no—
161Q8—68no—
162Q8C2×Q8×C911yescharacteristic
163C2×C4—24no—
164C2×C4—31no—
165C2×C4—31no—
166C2×C4—32no—
167C2×C4—32no—
168C2×C4—32no—
169C2×C4—34no—
170C2×C4—64no—
171C2×C4—62no—
172C2×C4#41⋊C914yes—
173C2×C4C22×C22⋊C914yes—
174C2×C4C22×C22⋊C912yes—
175C2×C3#557⋊C314yes—
176C2×C3C2×Q8×A411yescharacteristic
177C2×C3C22×#41⋊C311yescharacteristic
178C2×C3C2×2−1+4⋊C311yescharacteristic
179C22Q8×C22⋊C912yes—
180C22C2×#41⋊C912yes—
181C222−1+4⋊C912yes—
182C22C23×C22⋊C911yescharacteristic
183C4—24no—
184C4—31no—
185C4—31no—
186C4—32no—
187C4—64no—
188C4—62no—
189C4C2×#41⋊C914yes—
190C3C2×#557⋊C311yescharacteristic
191C2#557⋊C914yesdirect product factor
192C2C2×Q8×C22⋊C911yescharacteristic
193C2C22×#41⋊C911yescharacteristic
194C2C2×2−1+4⋊C911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C3C22×A4
commutatorC2×Q8C23×C9
FrattiniC22×C3C23×A4
FittingC2×C3×#557C3
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×C4⋊C4A4
hypocenterQ8C2×Q8×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2direct (N × H)
18. C2×Q8⋊C9Q8semidirect
21. C2×#557C9semidirect
46. Q8⋊C9C2×Q8semidirect
48. #557C2×C9semidirect
191. C2#557⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
#557⋊C92
C2×C4×Q8⋊C92
C2×C3×#5573
C2×C9×C4⋊C44