Finite Group Databasebeta

← #11901930

Subgroups — #11901930

Order 1152.

1494 conjugacy classes of subgroups; only the 590 normal subgroups are shown.

normal subgroups only

This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 590 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
1C9×#543C211yesmaximal, characteristic
2#10589725C2112yesmaximal, complemented
3#10589724C2112yesmaximal, complemented
4#10589585C213yesmaximal
5C2×#63439C213yesmaximal
6#86571—31nomaximal
7C23×Dic9C2211yescharacteristic
8C9×C22⋊Q8C22112yes—
9C2×C9×C22⋊C4C2213yes—
10C2×#3676C2213yes—
11Q8×Dic9C2214yescomplemented
12#63506C22112yescomplemented
13#63486C22112yes—
14C2×Dic9⋊C4C2216yes—
15C2×C4×Dic9C2216yes—
16#63451C22124yescomplemented
17#63450C22112yescomplemented
18#63449C22112yescomplemented
19#63440C22124yes—
20#63439C22112yes—
21#63439C22112yes—
22C3×#543D311yescharacteristic
23#5623—312no—
24#5622—312no—
25#5483—33no—
26C2×#877—33no—
27C24×C9C2311yescharacteristic
28C2×Q8×C9C2314yes—
29C22×C4×C9C2316yes—
30C22×Dic9Q818yescomplemented
31C22×Dic9C2316yes—
32C22×Dic9C2313yes—
33C22×Dic9C2313yes—
34C2×Dic18C23112yes—
35C9×C4⋊C4C23112yes—
36C9×C22⋊C4C23112yes—
37#3676C23112yes—
38C4⋊Dic9C23112yes—
39Dic9⋊C4C23124yes—
40Dic9⋊C4C23124yes—
41C4×Dic9C23112yes—
42C4×Dic9C23112yes—
43#3458—91noSylow
44C23×Dic3—31no—
45C3×C22⋊Q8C2×D3112yes—
46C2×C3×C22⋊C4C2×D313yes—
47C2×#217—33no—
48Q8×Dic3—34no—
49#944—312no—
50#924—312no—
51C2×Dic3⋊C4—36no—
52C2×C4×Dic3—36no—
53#889—324no—
54#888—312no—
55#887—312no—
56#878—324no—
57#877—312no—
58#877—312no—
59C23×C9—42no—
60C23×C9C2×Q814yes—
61C23×C9C2413yes—
62Q8×C9—44no—
63C2×C4×C9—46no—
64C2×C4×C9C24112yes—
65C2×Dic9—46no—
66C2×Dic9C2×Q8112yes—
67C2×Dic9C2×Q8112yes—
68C2×Dic9C24112yes—
69C2×Dic9C2411yescharacteristic
70C2×Dic9C2413yes—
71Dic18—412no—
72#544—912no—
73#543—93no—
74#543D911yescharacteristic
75#533—912no—
76C2×#117—93no—
77C24×C3C22×D311yescharacteristic
78C2×C3×Q8C22×D314yes—
79C22×C3×C4C22×D316yes—
80C22×Dic3—38no—
81C22×Dic3—33no—
82C22×Dic3—33no—
83C22×Dic3—36no—
84C2×Dic6—312no—
85C3×C4⋊C4C22×D3112yes—
86C3×C22⋊C4C22×D3112yes—
87#217—312no—
88C4⋊Dic3—312no—
89Dic3⋊C4—324no—
90Dic3⋊C4—324no—
91C4×Dic3—312no—
92C4×Dic3—312no—
93C22×C9—26no—
94C22×C9—44no—
95C22×C9C22×Q816yes—
96C22×C9C2511yescharacteristic
97C4×C9—212no—
98Dic9—212no—
99Dic9C22×Q812yes—
100Dic9C22×Q816yes—
101C23×C4—91no—
102C4⋊Q8—912no—
103C4⋊Q8—912no—
104#125—924no—
105C22⋊Q8—912no—
106C22⋊Q8—924no—
107C22⋊Q8C2×D9112yes—
108C4×Q8—94no—
109C4×Q8—912no—
110#117—912no—
111#117—912no—
112C2×C4⋊C4—96no—
113C2×C22⋊C4—93no—
114C2×C22⋊C4C2×D913yes—
115C2×C42—96no—
116C23×C3—42no—
117C23×C3D3×Q814yes—
118C23×C3C23×D313yes—
119C3×Q8—44no—
120C2×C3×C4—46no—
121C2×C3×C4C23×D3112yes—
122C2×Dic3—312no—
123C2×Dic3—312no—
124C2×Dic3—31no—
125C2×Dic3—33no—
126C2×Dic3—312no—
127C2×Dic3—126no—
128Dic6—1212no—
129C2×C9—26no—
130C2×C9C23×Q811yescharacteristic
131C2×C9#58512yes—
132C24C22×D911yescharacteristic
133C2×Q8—912no—
134C2×Q8C22×D914yes—
135C22×C4—98no—
136C22×C4—93no—
137C22×C4—93no—
138C22×C4—96no—
139C22×C4C22×D916yes—
140C4⋊C4—924no—
141C4⋊C4—924no—
142C4⋊C4—912no—
143C4⋊C4C22×D9112yes—
144C22⋊C4—912no—
145C22⋊C4C22×D9112yes—
146C42—912no—
147C42—912no—
148C22×C3—26no—
149C22×C3—44no—
150C22×C3C2×D3×Q816yes—
151C22×C3C24×D311yescharacteristic
152C3×C4—212no—
153Dic3—32no—
154Dic3—36no—
155Dic3—612no—
156C9#345811yescharacteristic, complemented, Sylow
157C23—42no—
158C23Q8×D914yes—
159C23C23×D913yes—
160Q8—44no—
161Q8—3612no—
162C2×C4—46no—
163C2×C4—91no—
164C2×C4—93no—
165C2×C4—912no—
166C2×C4—912no—
167C2×C4—912no—
168C2×C4—366no—
169C2×C4C23×D9112yes—
170C2×C3—26no—
171C2×C3C22×D3×Q811yescharacteristic
172C2×C3#596612yes—
173C22—26no—
174C22—44no—
175C22C2×Q8×D916yes—
176C22C24×D911yescharacteristic
177C4—212no—
178C4—92no—
179C4—96no—
180C4—1812no—
181C3#8657111yescharacteristic
182C2—26no—
183C2C22×Q8×D911yescharacteristic
184C2#1059314112yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#543C2
prime radicalC24×C3C22×D3
hypercenter#543D9
hypocenterC9#3458
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
2. #10589725C2semidirect
3. #10589724C2semidirect
11. Q8×Dic9C22semidirect
12. #63506C22semidirect
16. #63451C22semidirect
17. #63450C22semidirect
18. #63449C22semidirect
30. C22×Dic9Q8semidirect
156. C9#3458semidirect

Maximal subgroups

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

subgroupindex
C9×#5432
#105897252
#105897242
#105895852
C2×#634392
#865713