Finite Group Databasebeta

← #11874989

Subgroups — #11874989

Order 1152.

793 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 793 conjugacy classes of subgroups — too many to draw. Only its 200 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#10593866C212yesmaximal
2C4×C8×C3⋊D3C211yesmaximal, characteristic
3C3×#4680C212yesmaximal, complemented
4#10590874C214yesmaximal, complemented
5#10590712C214yesmaximal
6#10590312C212yesmaximal, complemented
7#81891—32nomaximal
8C2×C8×C3⋊D3C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×#869C2214yes—
11#63872C2214yes—
12#63871—24no—
13#63849C2214yes—
14#63843—24no—
15C32×C4×C8C2211yescharacteristic
16C8×C3⋊Dic3C2212yes—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#817C2218yes—
19#63576C2218yes—
20#5728—34no—
21C3×#498—32no—
22#5078—34no—
23#4860—38no—
24#4858—38no—
25C4×D3×C8—32no—
26C4×D3×C8—61no—
27#4680D312yescomplemented
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C3×Dic6—24no—
31C2×C32×C8C2312yes—
32C32×C42C2311yescharacteristic
33C4×C3⋊Dic3D412yes—
34C4×C3⋊Dic3C2311yescharacteristic
35C2×C3⋊(C3⋊C8)C2312yes—
36C8×C3⋊D3Q818yescomplemented
37C3×C4⋊Dic3—24no—
38C3×C4⋊Dic3C2318yes—
39Dic3⋊Dic3—28no—
40#3722—24no—
41Dic32—24no—
42#3160—91noSylow
43C3×C4⋊Q8—34no—
44#946—64no—
45Q8×Dic3—64no—
46C2×D3×C8—34no—
47C2×D3×C8—62no—
48#897—64no—
49#892—38no—
50#890—38no—
51#887—64no—
52C42×D3—32no—
53C42×D3—61no—
54#869C2×D314yes—
55C3×#106—38no—
56C3×C4×C8—21no—
57C3×C4×C8C2×D312yes—
58#817C2×D318yes—
59C8×Dic3—34no—
60C8×Dic3—62no—
61#807—316no—
62C4×C3⋊C8—32no—
63C4×C3⋊C8—61no—
64C22×C3⋊D3C2×D411yescharacteristic
65C2×C32×C4C2×D412yes—
66C2×C32×C4C2411yescharacteristic
67C2×C3⋊Dic3C2×D412yes—
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4×C3⋊D3—24no—
70C4×C3⋊D3C2×Q814yes—
71C2×C3×Dic3—28no—
72C3×Dic6—48no—
73C32×C8C2×Q814yes—
74C3⋊(C3⋊C8)C2×Q814yes—
75#533—92no—
76#500—92no—
77#499—94no—
78#498—32no—
79#427—94no—
80C2×C4×C8—91no—
81C2×C3×Q8—64no—
82C2×C4×D3—32no—
83C2×C4×D3—34no—
84C2×C4×D3—61no—
85C2×C4×D3—62no—
86C2×Dic6—24no—
87C2×C3×C8—22no—
88C2×C3×C8C22×D314yes—
89C3×C4⋊C4—38no—
90C3×C4⋊C4—64no—
91C3×C42—21no—
92C3×C42C22×D312yes—
93(C2×D3)⋊C4—68no—
94C4⋊Dic3—24no—
95C4⋊Dic3—68no—
96C4⋊Dic3C22×D318yes—
97Dic3⋊C4—68no—
98C4×Dic3—34no—
99C4×Dic3—32no—
100C4×Dic3—61no—
101C4×Dic3—62no—
102C4×Dic3—68no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—62no—
105D3×C8—316no—
106D3×C8—68no—
107C22×C32C22×D411yescharacteristic
108C2×C3⋊D3—22no—
109C2×C3⋊D3C4⋊Q812yes—
110C32×C4#13514yes—
111C32×C4C22×Q812yes—
112C3⋊Dic3—22no—
113C3⋊Dic3C4⋊Q812yes—
114C3×Dic3—48no—
115C22×C8—92no—
116C4⋊Q8—34no—
117#125—94no—
118C22⋊Q8—184no—
119C4×Q8—184no—
120#117—94no—
121C2×C42—91no—
122#107—98no—
123#106—38no—
124C4×C8—92no—
125C4×C8—91no—
126C4×C8D3211yescharacteristic
127C22×D3—32no—
128C22×D3—61no—
129C3×Q8—128no—
130C2×C3×C4—21no—
131C2×C3×C4—22no—
132C2×C3×C4—68no—
133C2×C3×C4D3×D414yes—
134C2×C3×C4C23×D312yes—
135C2×Dic3—28no—
136C2×Dic3—32no—
137C2×Dic3—34no—
138C2×Dic3—61no—
139C2×Dic3—62no—
140C4×D3—38no—
141C4×D3—64no—
142C4×D3—68no—
143C4×D3—68no—
144Dic6—48no—
145C3×C8—24no—
146C3×C8D3×Q818yes—
147C3⋊C8—38no—
148C3⋊C8—64no—
149C2×C32C2×C4⋊Q811yescharacteristic
150C2×C32C2×#13512yes—
151C3⋊D3—22no—
152C2×Q8—64no—
153C22×C4—91no—
154C22×C4—92no—
155C2×C8—92no—
156C2×C8—98no—
157C2×C8C2×D3212yes—
158C4⋊C4—38no—
159C4⋊C4—64no—
160C4⋊C4—188no—
161C22⋊C4—184no—
162C42—91no—
163C42—92no—
164C42—184no—
165C42C2×D3211yescharacteristic
166C22×C3—21no—
167C22×C3C2×D3×D412yes—
168C2×D3—34no—
169C2×D3—62no—
170C2×D3—64no—
171C2×D3—64no—
172C3×C4—22no—
173C3×C4—24no—
174C3×C4—128no—
175C3×C4#91618yes—
176C3×C4C2×D3×Q814yes—
177Dic3—34no—
178Dic3—48no—
179Dic3—62no—
180Dic3—64no—
181Dic3—64no—
182C32#316011yescharacteristic, complemented, Sylow
183C23—91no—
184Q8—128no—
185C2×C4—68no—
186C2×C4—91no—
187C2×C4—94no—
188C2×C4—92no—
189C2×C4—184no—
190C2×C4#380212yes—
191C2×C4C22×D3211yescharacteristic
192C8—94no—
193C8#379714yes—
194C2×C3—21no—
195C2×C3—22no—
196C2×C3D3×C4⋊Q812yes—
197C2×C3C2×#91614yes—
198D3—64no—
199D3—64no—
200C22—92no—
201C22—182no—
202C22C2×#380211yescharacteristic
203C4—92no—
204C4—128no—
205C4—182no—
206C4#6380914yes—
207C4C2×#379712yes—
208C3—21no—
209C3#8189112yescomplemented
210C2—182no—
211C2#1059390911yescharacteristic
212C2C2×#6380912yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C3×#4680C2semidirect
4. #10590874C2semidirect
6. #10590312C2semidirect
27. #4680D3semidirect
36. C8×C3⋊D3Q8semidirect
182. C32#3160semidirect
209. C3#81891semidirect

Maximal subgroups

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

subgroupindex
#105938662
C4×C8×C3⋊D32
C3×#46802
#105908742
#105907122
#105903122
#818913