Finite Group Databasebeta

← #11901931

Subgroups — #11901931

Order 1152.

2988 conjugacy classes of subgroups; only the 833 normal subgroups are shown.

normal subgroups only

This group has 2988 conjugacy classes of subgroups — too many to draw. Only its 833 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×#543C211yesmaximal, characteristic
2#10596094C2112yesmaximal, complemented
3#10596093C2112yesmaximal, complemented
4#10595954C213yesmaximal
5C2×#64086C213yesmaximal
6#86571—34nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C32×C22⋊Q8C22112yes—
9C2×C32×C22⋊C4C2213yes—
10C2×#3757C2213yes—
11Q8×C3⋊Dic3C2214yescomplemented
12#64153C22112yescomplemented
13#64133C22112yes—
14C2×#3750C2216yes—
15C2×C4×C3⋊Dic3C2216yes—
16#64098C22124yescomplemented
17#64097C22112yescomplemented
18#64096C22112yescomplemented
19#64087C22124yes—
20#64086C22112yes—
21#64086C22112yes—
22C3×#543D314yes—
23#5623—348no—
24#5622—348no—
25#5483—312no—
26C2×#877—312no—
27C24×C32C2311yescharacteristic
28C2×C32×Q8C2314yes—
29C22×C32×C4C2316yes—
30C22×C3⋊Dic3Q818yescomplemented
31C22×C3⋊Dic3C2316yes—
32C22×C3⋊Dic3C2313yes—
33C22×C3⋊Dic3C2313yes—
34C2×#634C23112yes—
35C32×C4⋊C4C23112yes—
36C32×C22⋊C4C23112yes—
37#3757C23112yes—
38C4⋊(C3⋊Dic3)C23112yes—
39#3750C23124yes—
40#3750C23124yes—
41C4×C3⋊Dic3C23112yes—
42C4×C3⋊Dic3C23112yes—
43#3458—91noSylow
44C23×Dic3—34no—
45C3×C22⋊Q8C2×D3148yes—
46C2×C3×C22⋊C4C2×D3112yes—
47C2×#217—312no—
48Q8×Dic3—316no—
49#944—348no—
50#924—348no—
51C2×Dic3⋊C4—324no—
52C2×C4×Dic3—324no—
53#889—396no—
54#888—348no—
55#887—348no—
56#878—396no—
57#877—348no—
58#877—348no—
59C23×C32—42no—
60C23×C32C2×Q814yes—
61C23×C32C2413yes—
62C32×Q8—44no—
63C2×C32×C4—46no—
64C2×C32×C4C24112yes—
65C2×C3⋊Dic3—46no—
66C2×C3⋊Dic3C2×Q8112yes—
67C2×C3⋊Dic3C2×Q8112yes—
68C2×C3⋊Dic3C24112yes—
69C2×C3⋊Dic3C2411yescharacteristic
70C2×C3⋊Dic3C2413yes—
71#634—412no—
72#544—912no—
73#543—93no—
74#543C3⋊D311yescharacteristic
75#533—912no—
76C2×#117—93no—
77C24×C3C22×D314yes—
78C2×C3×Q8C22×D3116yes—
79C22×C3×C4C22×D3124yes—
80C22×Dic3—332no—
81C22×Dic3—312no—
82C22×Dic3—312no—
83C22×Dic3—324no—
84C2×Dic6—348no—
85C3×C4⋊C4C22×D3148yes—
86C3×C22⋊C4C22×D3148yes—
87#217—348no—
88C4⋊Dic3—348no—
89Dic3⋊C4—396no—
90Dic3⋊C4—396no—
91C4×Dic3—348no—
92C4×Dic3—348no—
93C22×C32—26no—
94C22×C32—44no—
95C22×C32C22×Q816yes—
96C22×C32C2511yescharacteristic
97C32×C4—212no—
98C3⋊Dic3—212no—
99C3⋊Dic3C22×Q812yes—
100C3⋊Dic3C22×Q816yes—
101C23×C4—91no—
102C4⋊Q8—912no—
103C4⋊Q8—912no—
104#125—924no—
105C22⋊Q8—912no—
106C22⋊Q8—924no—
107C22⋊Q8C2×C3⋊D3112yes—
108C4×Q8—94no—
109C4×Q8—912no—
110#117—912no—
111#117—912no—
112C2×C4⋊C4—96no—
113C2×C22⋊C4—93no—
114C2×C22⋊C4C2×C3⋊D313yes—
115C2×C42—96no—
116C23×C3—48no—
117C23×C3D3×Q8116yes—
118C23×C3C23×D3112yes—
119C3×Q8—416no—
120C2×C3×C4—424no—
121C2×C3×C4C23×D3148yes—
122C2×Dic3—348no—
123C2×Dic3—348no—
124C2×Dic3—34no—
125C2×Dic3—312no—
126C2×Dic3—348no—
127C2×Dic3—1224no—
128Dic6—1248no—
129C2×C32—26no—
130C2×C32C23×Q811yescharacteristic
131C2×C32#58512yes—
132C24C22×C3⋊D311yescharacteristic
133C2×Q8—912no—
134C2×Q8C22×C3⋊D314yes—
135C22×C4—93no—
136C22×C4—93no—
137C22×C4—98no—
138C22×C4—96no—
139C22×C4C22×C3⋊D316yes—
140C4⋊C4—924no—
141C4⋊C4—924no—
142C4⋊C4—912no—
143C4⋊C4C22×C3⋊D3112yes—
144C22⋊C4—912no—
145C22⋊C4C22×C3⋊D3112yes—
146C42—912no—
147C42—912no—
148C22×C3—224no—
149C22×C3—416no—
150C22×C3C2×D3×Q8124yes—
151C22×C3C24×D314yes—
152C3×C4—248no—
153Dic3—38no—
154Dic3—324no—
155Dic3—648no—
156C32#345811yescharacteristic, complemented, Sylow
157C23—42no—
158C23Q8×C3⋊D314yes—
159C23C23×C3⋊D313yes—
160Q8—44no—
161Q8—3612no—
162C2×C4—46no—
163C2×C4—912no—
164C2×C4—912no—
165C2×C4—91no—
166C2×C4—93no—
167C2×C4—912no—
168C2×C4—366no—
169C2×C4C23×C3⋊D3112yes—
170C2×C3—224no—
171C2×C3C22×D3×Q814yes—
172C2×C3#596618yes—
173C22—26no—
174C22—44no—
175C22C2×Q8×C3⋊D316yes—
176C22C24×C3⋊D311yescharacteristic
177C4—212no—
178C4—92no—
179C4—96no—
180C4—1812no—
181C3#8657114yescomplemented
182C2—26no—
183C2C22×Q8×C3⋊D311yescharacteristic
184C2#1059675812yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#543C2
prime radicalC24×C32C23
hypercenter#543C3⋊D3
hypocenterC32#3458
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
2. #10596094C2semidirect
3. #10596093C2semidirect
11. Q8×C3⋊Dic3C22semidirect
12. #64153C22semidirect
16. #64098C22semidirect
17. #64097C22semidirect
18. #64096C22semidirect
30. C22×C3⋊Dic3Q8semidirect
156. C32#3458semidirect
181. C3#86571semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
#105960942
#105960932
#105959542
C2×#640862
#865713