Finite Group Databasebeta

← #11795347

Subgroups — #11795347

Order 1152.

409 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 409 conjugacy classes of subgroups — too many to draw. Only its 112 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#10592818C211yesmaximal, characteristic
2#10591130C212yesmaximal
3C2×#63574C211yesmaximal, characteristic
4C3×#4554C212yesmaximal
5#10589165C211yesmaximal, characteristic
6#68981—32nomaximal
7C2×C32×M16C2211yescharacteristic
8#64135C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12#63641—22no—
13#63575—22no—
14#63574—22no—
15#63573—22no—
16#5121—32no—
17#5119—32no—
18#5119—61no—
19#4964—32no—
20C2×#808—32no—
21C3×#343—32no—
22#4558—32no—
23#4554D312yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3×Dic3—22no—
26C32×M16—22no—
27C2×C32×C8—21no—
28#3757—21no—
29C4⋊(C3⋊Dic3)D412yes—
30C4×C3⋊Dic3—21no—
31C2×C3⋊(C3⋊C8)—22no—
32C2×C3⋊(C3⋊C8)D412yes—
33C3×C4⋊Dic3—22no—
34C3×C4⋊Dic3—22no—
35C3×#208—22no—
36C3×#208Q814yes—
37C2×C3×C3⋊C8—22no—
38#2090—91noSylow
39C2×C3×M16—21no—
40C2×C3×M16—32no—
41C2×C3×M16C2×D312yes—
42C2×C3×C4⋊C4—32no—
43#926—32no—
44#926—61no—
45C2×C4⋊Dic3C2×D312yes—
46C2×#208C2×D312yes—
47C22×C3⋊C8—32no—
48C22×C3⋊C8—61no—
49#818—62no—
50#817—62no—
51Dic3⋊C8—64no—
52Dic3⋊C8—64no—
53#808—62no—
54#808—64no—
55#807—62no—
56C23×C32#4111yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4C2×Q812yes—
60C2×C32×C4#4112yes—
61C2×C3⋊Dic3—22no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—82no—
64C32×C8—41no—
65C3⋊(C3⋊C8)—22no—
66C3×C3⋊C8—24no—
67#428—92no—
68C2×#106—91no—
69#424—91no—
70#343—32no—
71#341—91no—
72C22×C3×C4—21no—
73C22×C3×C4—62no—
74C22×C3×C4C22×D312yes—
75C22×Dic3—22no—
76C3×M16—22no—
77C3×M16—22no—
78C3×M16—34no—
79C3×M16—42no—
80C3×M16—62no—
81C2×C3×C8—22no—
82C2×C3×C8—22no—
83C2×C3×C8—62no—
84C3×C4⋊C4—62no—
85C3×C4⋊C4—62no—
86#217—62no—
87#217—62no—
88C4⋊Dic3—22no—
89C4⋊Dic3—22no—
90C4⋊Dic3—32no—
91C4⋊Dic3—32no—
92C4⋊Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95#208—22no—
96#208Dic614yes—
97C2×C3⋊C8—22no—
98C2×C3⋊C8—34no—
99C2×C3⋊C8—62no—
100C2×C3⋊C8—62no—
101C2×C3⋊C8—62no—
102C2×C3⋊C8—122no—
103C22×C32—22no—
104C22×C32#12111yescharacteristic
105C22×C32#12512yes—
106C32×C4C22⋊Q812yes—
107C32×C4#12311yescharacteristic
108C32×C4C4⋊Q811yescharacteristic
109C3⋊Dic3—42no—
110C3×Dic3—82no—
111C2×M16—32no—
112C2×M16D3211yescharacteristic
113C22×C8—91no—
114#117—91no—
115C2×C4⋊C4—32no—
116#107—182no—
117#106—182no—
118#106—182no—
119C4⋊C8—182no—
120C23×C3—21no—
121C23×C3#23512yes—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—122no—
127C2×C3×C4—242no—
128C2×C3×C4C2×Dic612yes—
129C2×C3×C4#23512yes—
130C2×C3×C4D3×D412yes—
131C2×C3×C4D3×D412yes—
132C2×C3×C4#23712yes—
133C2×C3×C4D3×Q812yes—
134C2×Dic3—42no—
135C2×Dic3—64no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—82no—
139C3×C8—42no—
140C3×C8—42no—
141C3×C8—64no—
142C3⋊C8—24no—
143C3⋊C8—64no—
144C3⋊C8—122no—
145C2×C32—22no—
146C2×C32#39811yescharacteristic
147C2×C32#47112yes—
148C22×C4—62no—
149C22×C4C2×D3211yescharacteristic
150M16—22no—
151M16—34no—
152M16—62no—
153C2×C8—21no—
154C2×C8—62no—
155C2×C8—92no—
156C2×C8—182no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C4⋊C4—92no—
160C22⋊C4—181no—
161C42—181no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—22no—
165C22×C3—21no—
166C22×C3—42no—
167C22×C3#87012yes—
168C22×C3#88412yes—
169C22×C3#88912yes—
170C3×C4—21no—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—242no—
174C3×C4#87812yes—
175C3×C4#88312yes—
176C3×C4#88812yes—
177C3×C4#89612yes—
178Dic3—82no—
179Dic3—124no—
180Dic3—122no—
181Dic3—122no—
182C32#209011yescharacteristic, complemented, Sylow
183C23#379811yescharacteristic
184C2×C4—122no—
185C2×C4—182no—
186C2×C4—242no—
187C2×C4D3×Dic612yes—
188C2×C4#380211yescharacteristic
189C2×C4#380412yes—
190C2×C4#381111yescharacteristic
191C8—41no—
192C8—64no—
193C8—182no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—21no—
198C2×C3—42no—
199C2×C3#465712yes—
200C2×C3#474812yes—
201C2×C3#475412yes—
202C22—22no—
203C22#6386712yes—
204C22#6391211yescharacteristic
205C4—242no—
206C4—362no—
207C4#6384011yescharacteristic
208C4#6389912yes—
209C4#6397511yescharacteristic
210C3—21no—
211C3#6898112yescomplemented
212C2—22no—
213C2#1059099112yes—
214C2#1059135611yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC23×C32#41
hypercenterC2×M16D32
hypocenterC32#2090
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
182. C32#2090semidirect
211. C3#68981semidirect

Maximal subgroups

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

subgroupindex
#105928182
#105911302
C2×#635742
C3×#45542
#105891652
#689813