Finite Group Databasebeta

← #11922888

Subgroups — #11922888

Order 1152.

484 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C3×C4×#41⋊C3C211yesmaximal, characteristic
2#10593660C212yesmaximal
3#10593623C214yesmaximal, complemented
4#85339—33nomaximal
5#82509—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64079—41nomaximal
8C3×C4×SL(2,𝔽3)C2212yes—
9C3⋊#859C2214yes—
10C3×C4×#41D311yescharacteristic
11C2×#870—31no—
12C4×#41⋊C3D313yes—
13#5426—36no—
14#5389—312no—
15#5232—32no—
16#5022—34no—
17#5009—34no—
18#4995—32no—
19#4924—31no—
20C3×#41⋊C3Q812yes—
21C2×C3×SL(2,𝔽3)C2311yescharacteristic
22C32×C42—41no—
23C4⋊(C3⋊Dic3)—42no—
24#3750—44no—
25#3080—91noSylow
26C2×C3×#41C2×D311yescharacteristic
27C2×#41⋊C3C2×D313yes—
28C3×C4×Q8C2×D312yes—
29C3×C4×D4—32no—
30C3×#117—31no—
31C2×C3×C42—31no—
32C2×C4⋊Dic3—32no—
33C2×Dic3⋊C4—62no—
34C2×#208—32no—
35#870—34no—
36#870—61no—
37#870—61no—
38#870—123no—
39C4×SL(2,𝔽3)C2×D316yes—
40#859—312no—
41#835—34no—
42#832—34no—
43#808—34no—
44#807—34no—
45C4⋊(C3⋊C8)—34no—
46C2×C32×C4—41no—
47C2×C32×C4—42no—
48C2×C3⋊Dic3—44no—
49C3×SL(2,𝔽3)C2×Q811yescharacteristic
50C2×#125—91no—
51C4×#41C3⋊D311yescharacteristic
52#479—94no—
53#478—94no—
54#428—92no—
55#423—91no—
56#417—92no—
57C3×#41—32no—
58C3×#41Dic612yes—
59C2×C3×Q8C22×D311yescharacteristic
60C2×C3×D4—31no—
61C22×C3×C4—31no—
62C22×C3×C4—32no—
63C22×Dic3—62no—
64#41⋊C3Dic616yes—
65C2×SL(2,𝔽3)C22×D313yes—
66C3×C4⋊C4—32no—
67C3×C22⋊C4—61no—
68C3×C42—32no—
69C3×C42—31no—
70C3×C42—43no—
71C3×C42S411yescharacteristic
72C4⋊Dic3—34no—
73C4⋊Dic3—62no—
74C4⋊Dic3—126no—
75Dic3⋊C4—64no—
76Dic3⋊C4—64no—
77Dic3⋊C4—1212no—
78#208—64no—
79C2×C3⋊C8—34no—
80C22×C32—41no—
81C32×C4—42no—
82C32×C4—82no—
83C3⋊Dic3—84no—
84C2×#41C2×C3⋊D311yescharacteristic
85C2×M16—92no—
86#125—94no—
87#125—181no—
88#125—181no—
89C4×Q8C2×C3⋊D312yes—
90C4×D4—32no—
91#117—31no—
92C2×C4⋊C4—92no—
93C2×C4⋊C4—182no—
94C2×C42—31no—
95#107—94no—
96#106—94no—
97C4⋊C8—94no—
98#103—94no—
99#102—94no—
100C23×C3—31no—
101C3×Q8—31no—
102C3×Q8C2×Dic611yescharacteristic
103C3×D4—32no—
104C3×D4—61no—
105C2×C3×C4—31no—
106C2×C3×C4—32no—
107C2×C3×C4—32no—
108C2×C3×C4—32no—
109C2×C3×C4—43no—
110C2×C3×C4—46no—
111C2×C3×C4—122no—
112C2×C3×C4C2×S412yes—
113C2×C3×C4C2×S411yescharacteristic
114C2×Dic3—64no—
115C2×Dic3—1212no—
116C2×Dic3—124no—
117SL(2,𝔽3)C2×Dic613yes—
118C3⋊C8—64no—
119C2×C32—41no—
120C2×C32—42no—
121#41—32no—
122#41#63412yes—
123C2×Q8C22×C3⋊D311yescharacteristic
124C2×D4—31no—
125C22×C4—31no—
126C22×C4—32no—
127C22×C4—182no—
128M16—184no—
129C2×C8—94no—
130C4⋊C4—32no—
131C4⋊C4—94no—
132C4⋊C4—184no—
133C4⋊C4—182no—
134C4⋊C4—184no—
135C22⋊C4—61no—
136C42—32no—
137C42—31no—
138C42C3⋊S411yescharacteristic
139C22×C3—32no—
140C22×C3—43no—
141C22×C3—62no—
142C22×C3C22×S411yescharacteristic
143C3×C4—22no—
144C3×C4—31no—
145C3×C4—31no—
146C3×C4—46no—
147C3×C4—62no—
148C3×C4—86no—
149C3×C4A4⋊Q812yes—
150Dic3—124no—
151Dic3—2412no—
152C32—41noSylow
153C23—31no—
154Q8—31no—
155Q8C2×#63411yescharacteristic
156D4—32no—
157D4—61no—
158C2×C4—31no—
159C2×C4—32no—
160C2×C4—32no—
161C2×C4—32no—
162C2×C4—122no—
163C2×C4—184no—
164C2×C4—364no—
165C2×C4C2×C3⋊S412yes—
166C2×C4C2×C3⋊S411yescharacteristic
167C8—184no—
168C2×C3—43no—
169C2×C3—46no—
170C2×C3—62no—
171C2×C3C2×A4⋊Q811yescharacteristic
172C2×C3#592312yes—
173C22—32no—
174C22—62no—
175C22C22×C3⋊S411yescharacteristic
176C4—22no—
177C4—31no—
178C4—31no—
179C4—62no—
180C4—364no—
181C4#6425912yes—
182C3—43no—
183C3#8533911yescharacteristic, complemented
184C2—62no—
185C2C2×#6425911yescharacteristic
186C2#1059658612yes—
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
hypercenterC42C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10593623C2semidirect
183. C3#85339semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#41⋊C32
#105936602
#105936232
#853393
#825093
#640794