Finite Group Databasebeta

← 2−1+4×C22⋊C9 #11919877

Subgroups — 2−1+4×C22⋊C9 #11919877

Order 1152.

2298 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 2298 conjugacy classes of subgroups — too many to draw. Only its 340 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#41×C22⋊C9C2110yesmaximal, complemented
2C2×Q8×C22⋊C9C215yesmaximal, complemented
3C22×C3×2−1+4C311yesmaximal, characteristic
4C9×2−1+4—41nomaximal
5Q8×C22⋊C9C22110yes—
6D4×C22⋊C9C22110yes—
7C2×C4×C22⋊C9C22115yes—
8C2×C3×2−1+4—310no—
9C2×C3×2−1+4—35no—
10C2×C3×2−1+4—31no—
11C22×C3×#41C2×C3110yes—
12C23×C3×Q8C2×C315yes—
13C22×C22⋊C9C2315yes—
14C9×#41—410no—
15C2×Q8×C9—45no—
16C4×C22⋊C9C23110yes—
17C22×2−1+4C911yescharacteristic, complemented, Sylow
18C3×2−1+4—320no—
19C3×2−1+4—330no—
20C3×2−1+4—320no—
21C3×2−1+4—310no—
22C3×2−1+4—35no—
23C3×2−1+4A411yescharacteristic
24C2×C3×#41—330no—
25C2×C3×#41—330no—
26C2×C3×#41—310no—
27C2×C3×#41—310no—
28C22×C3×Q8—315no—
29C22×C3×Q8—320no—
30C22×C3×Q8—35no—
31C22×C3×Q8C22×C3110yes—
32C22×C3×D4C22×C3110yes—
33C23×C3×C4C22×C3115yes—
34C2×C22⋊C9—25no—
35C2×C22⋊C9C2411yescharacteristic
36Q8×C9—410no—
37D4×C9—410no—
38C2×C4×C9—415no—
39C2×2−1+4—310no—
40C2×2−1+4—35no—
41C2×2−1+4—31no—
42C22×#41C2×C9110yescomplemented
43C23×Q8C2×C915yescomplemented
44C24×C3C23×C315yes—
45C3×#41—360no—
46C3×#41—360no—
47C3×#41—320no—
48C3×#41—310no—
49C3×#41—330no—
50C3×#41—330no—
51C3×#41C2×A4110yes—
52C2×C3×Q8—330no—
53C2×C3×Q8—360no—
54C2×C3×Q8—310no—
55C2×C3×Q8—310no—
56C2×C3×Q8—320no—
57C2×C3×Q8—315no—
58C2×C3×Q8C2×A415yes—
59C2×C3×D4—310no—
60C2×C3×D4—310no—
61C2×C3×D4—320no—
62C22×C3×C4—315no—
63C22×C3×C4—315no—
64C22×C3×C4—330no—
65C22×C3×C4C23×C3110yes—
66C22×C9—45no—
67C22⋊C92−1+411yescharacteristic, direct product factor
68C4×C9—410no—
692−1+4—320no—
702−1+4—330no—
712−1+4—320no—
722−1+4—310no—
732−1+4—35no—
742−1+4C22⋊C911yescharacteristic, direct product factor
75C2×#41—330no—
76C2×#41—330no—
77C2×#41—310no—
78C2×#41—310no—
79C22×Q8—315no—
80C22×Q8—320no—
81C22×Q8—35no—
82C22×Q8C22×C9110yes—
83C22×D4C22×C9110yes—
84C23×C4C22×C9115yes—
85C23×C3—25no—
86C23×C3—35no—
87C23×C3—35no—
88C23×C3—65no—
89C23×C3C24×C311yescharacteristic
90C3×Q8—320no—
91C3×Q8—330no—
92C3×Q8C22×A4110yes—
93C3×D4—320no—
94C3×D4—320no—
95C3×D4—310no—
96C3×D4C22×A4110yes—
97C2×C3×C4—330no—
98C2×C3×C4—315no—
99C2×C3×C4—310no—
100C2×C3×C4—330no—
101C2×C3×C4—310no—
102C2×C3×C4C22×A4115yes—
103C2×C9—41no—
104C2×C9—85no—
105C24C23×C915yes—
106#41—360no—
107#41—360no—
108#41—320no—
109#41—310no—
110#41—330no—
111#41—330no—
112#41C2×C22⋊C9110yescomplemented
113C2×Q8—330no—
114C2×Q8—360no—
115C2×Q8—310no—
116C2×Q8—310no—
117C2×Q8—320no—
118C2×Q8—315no—
119C2×Q8C2×C22⋊C915yescomplemented
120C2×D4—310no—
121C2×D4—310no—
122C2×D4—320no—
123C22×C4—315no—
124C22×C4—315no—
125C22×C4—330no—
126C22×C4C23×C9110yes—
127C22×C3—31no—
128C22×C3—31no—
129C22×C3—35no—
130C22×C3—65no—
131C22×C3—65no—
132C22×C3—65no—
133C22×C3—65no—
134C22×C3C3×2−1+411yescharacteristic
135C22×C3C23×A415yes—
136C3×C4—310no—
137C3×C4C23×A4110yes—
138C9—41noSylow
139C23—25no—
140C23—35no—
141C23—35no—
142C23—65no—
143C23C24×C911yescharacteristic
144Q8—320no—
145Q8—330no—
146Q8C22×C22⋊C9110yes—
147D4—320no—
148D4—320no—
149D4—310no—
150D4C22×C22⋊C9110yes—
151C2×C4—330no—
152C2×C4—315no—
153C2×C4—310no—
154C2×C4—330no—
155C2×C4—310no—
156C2×C4C22×C22⋊C9115yes—
157C2×C3—25no—
158C2×C3—31no—
159C2×C3—31no—
160C2×C3—65no—
161C2×C3C24×A411yescharacteristic
162C22—31no—
163C22—31no—
164C22—35no—
165C22—65no—
166C22—65no—
167C22—65no—
168C22—65no—
169C22C9×2−1+411yescharacteristic, complemented
170C22C23×C22⋊C915yes—
171C4—310no—
172C4C23×C22⋊C9110yes—
173C3A4×2−1+411yescharacteristic
174C2—25no—
175C2—31no—
176C2—31no—
177C2—65no—
178C2C24×C22⋊C911yescharacteristic
subgroupG/H
center, FrattiniC2×C3C24×A4
commutatorC23C24×C9
Fitting, prime radicalC22×C3×2−1+4C3
socle, cosocleC23×C3C24×C3
hypercenterC3×2−1+4A4
hypocenterC22C9×2−1+4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3 ◁ C3×2−1+4

Complements

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

NH ≅ G/Ntype
1. #41×C22⋊C9C2semidirect
2. C2×Q8×C22⋊C9C2semidirect
17. C22×2−1+4C9semidirect
42. C22×#41C2×C9semidirect
43. C23×Q8C2×C9semidirect
67. C22⋊C92−1+4direct (N × H)
74. 2−1+4C22⋊C9direct (N × H)
112. #41C2×C22⋊C9semidirect
119. C2×Q8C2×C22⋊C9semidirect
169. C22C9×2−1+4semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊C92
C2×Q8×C22⋊C92
C22×C3×2−1+43
C9×2−1+44