Finite Group Databasebeta

← #11794278

Subgroups — #11794278

Order 1152.

690 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 191 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#10595971C211yesmaximal, characteristic
2#10592820C212yesmaximal
3#10592676C211yesmaximal, characteristic
4C32×#343C211yesmaximal, characteristic
5#10589421C212yesmaximal
6#68979—34nomaximal
7C2×C32×M16C2212yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9#64135C2212yes—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133—22no—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64099—22no—
14#64097—22no—
15#63658—22no—
16#63645—22no—
17#63644—22no—
18#5500—34no—
19#5121—38no—
20#4977—34no—
21C3×#343D314yes—
22#4555—38no—
23C22×C32×C4D412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3—21no—
27C2×#634—22no—
28C32×M16—22no—
29C32×M16Q814yescomplemented
30C2×C32×C8—22no—
31C32×C4⋊C4—22no—
32#3757—22no—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)D412yes—
36C4⋊(C3⋊Dic3)D412yes—
37#3750—24no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3Q812yescomplemented
41#2061—91noSylow
42C2×C3×M16C2×D318yes—
43C2×C3×C4⋊C4C2×D314yes—
44#926—38no—
45C2×C4⋊Dic3—34no—
46#924—68no—
47C2×C4×Dic3—34no—
48#890—68no—
49#888—68no—
50C3⋊#95—68no—
51#818—68no—
52#817—68no—
53C23×C32C2×D411yescharacteristic
54C2×C32×C4—22no—
55C2×C32×C4—42no—
56C2×C32×C4C2×D412yes—
57C2×C32×C4C2×Q812yes—
58C2×C32×C4C2×Q811yescharacteristic
59C2×C32×C4#4111yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3—41no—
67#634—82no—
68C32×C8—24no—
69#544—91no—
70#428—92no—
71#382—91no—
72#343C3⋊D311yescharacteristic
73#339—92no—
74C22×C3×C4D1218yes—
75C22×C3×C4C22×D314yes—
76C22×Dic3—64no—
77C22×Dic3—64no—
78C2×Dic6—68no—
79C3×M16—28no—
80C3×M16Dic6116yescomplemented
81C2×C3×C8—28no—
82C3×C4⋊C4—28no—
83#217—68no—
84C4⋊Dic3—38no—
85C4⋊Dic3—38no—
86C4⋊Dic3—68no—
87C4⋊Dic3—68no—
88Dic3⋊C4—616no—
89C4×Dic3—38no—
90C4×Dic3—68no—
91C4×Dic3—64no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32#12011yescharacteristic
95C22×C32C22⋊Q811yescharacteristic
96C22×C32C4⋊Q811yescharacteristic
97C32×C4—42no—
98C32×C4C22⋊Q812yes—
99C32×C4C4⋊Q812yes—
100C3⋊Dic3—42no—
101C3⋊Dic3—42no—
102C3⋊Dic3—42no—
103C3⋊Dic3—81no—
104C2×M16C2×C3⋊D312yes—
105C4⋊Q8—182no—
106#125—182no—
107C22⋊Q8—182no—
108#117—92no—
109C2×C4⋊C4—91no—
110C2×C4⋊C4C2×C3⋊D311yescharacteristic
111C2×C42—91no—
112#107—182no—
113#106—182no—
114#95—182no—
115C23×C3C2×D1214yes—
116C2×C3×C4—28no—
117C2×C3×C4—48no—
118C2×C3×C4C2×Dic618yes—
119C2×C3×C4D3×D418yes—
120C2×C3×C4#23714yes—
121C2×C3×C4D3×Q814yes—
122C2×Dic3—68no—
123C2×Dic3—68no—
124C2×Dic3—68no—
125C2×Dic3—124no—
126C2×Dic3—124no—
127C2×Dic3—128no—
128C2×Dic3—124no—
129Dic6—248no—
130C3×C8—216no—
131C2×C32—21no—
132C2×C32—21no—
133C2×C32#39511yescharacteristic
134C2×C32#45411yescharacteristic
135C2×C32#45511yescharacteristic
136C2×Q8—182no—
137C22×C4—181no—
138C22×C4—181no—
139C22×C4C4⋊(C3⋊D3)12yes—
140C22×C4C22×C3⋊D311yescharacteristic
141M16—22no—
142M16#63414yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—92no—
146C4⋊C4—92no—
147C4⋊C4—182no—
148C4⋊C4—184no—
149C4⋊C4—182no—
150C22⋊C4—182no—
151C42—92no—
152C42—182no—
153C42—181no—
154C22×C3—24no—
155C22×C3—24no—
156C22×C3#86914yes—
157C22×C3#88214yes—
158C22×C3#89714yes—
159C3×C4—48no—
160C3×C4#87818yes—
161C3×C4#88818yes—
162Dic3—128no—
163Dic3—128no—
164Dic3—128no—
165Dic3—244no—
166C32#206111yescharacteristic, complemented, Sylow
167C23C2×C4⋊(C3⋊D3)11yescharacteristic
168Q8—722no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—182no—
172C2×C4—182no—
173C2×C4—182no—
174C2×C4—361no—
175C2×C4—361no—
176C2×C4—362no—
177C2×C4—361no—
178C2×C4C2×#63412yes—
179C2×C4D4×C3⋊D312yes—
180C2×C4#383011yescharacteristic
181C2×C4Q8×C3⋊D311yescharacteristic
182C8—24no—
183C2×C3—24no—
184C2×C3—24no—
185C2×C3#465614yes—
186C2×C3#474614yes—
187C2×C3#475314yes—
188C22—21no—
189C22—21no—
190C22#6407811yescharacteristic
191C22#6409111yescharacteristic
192C22#6410611yescharacteristic
193C4—42no—
194C4—362no—
195C4—362no—
196C4—362no—
197C4—721no—
198C4#6408712yes—
199C4#6409712yes—
200C3#6897914yescomplemented
201C2—21no—
202C2—21no—
203C2#1059235511yescharacteristic
204C2#1059244511yescharacteristic
205C2#1059245211yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#343C3⋊D3
hypocenterC32#2061
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
29. C32×M16Q8semidirect
40. C4×C3⋊Dic3Q8semidirect
80. C3×M16Dic6semidirect
142. M16#634semidirect
166. C32#2061semidirect
200. C3#68979semidirect

Maximal subgroups

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

subgroupindex
#105959712
#105928202
#105926762
C32×#3432
#105894212
#689793