Finite Group Databasebeta

← #11786173

Subgroups — #11786173

Order 1152.

395 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 395 conjugacy classes of subgroups — too many to draw. Only its 108 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
1M16×C3⋊Dic3C211yesmaximal, characteristic
2C3×#4556C212yesmaximal
3#10589160C212yesmaximal
4#10589159C211yesmaximal, characteristic
5#10589157C211yesmaximal, characteristic
6#69017—32nomaximal
7C2×C32×M16C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×#208C2212yes—
12#63642C412yescomplemented
13C8×C3⋊Dic3C412yescomplemented
14Dic3×M16—32no—
15Dic3×M16—61no—
16C3×#344—32no—
17C3⋊#338—32no—
18#4556D312yes—
19#4555—32no—
20#4532—32no—
21#4531—32no—
22C22×C32×C4C2311yescharacteristic
23C22×C3⋊Dic3—21no—
24C32×M16—22no—
25C2×C32×C8C2×C412yes—
26C4×C3⋊Dic3—21no—
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3C2×C411yescharacteristic
29#3748—22no—
30C2×C3⋊(C3⋊C8)C2×C412yes—
31C3×#217—22no—
32C3×C4⋊Dic3—22no—
33C3×C4×Dic3—22no—
34C3×#208—22no—
35C3×#208—22no—
36C2×C3×C3⋊C8—22no—
37#1841—91noSylow
38C2×C3×M16—21no—
39C2×C3×M16—32no—
40C2×C3×M16C2×D312yes—
41C3×#117—32no—
42#926C2×D312yes—
43C2×C4×Dic3—32no—
44C2×C4×Dic3—61no—
45C2×#208—32no—
46C2×#208—61no—
47C2×#208C2×D312yes—
48#815—34no—
49#815—62no—
50C8×Dic3—34no—
51C8×Dic3—62no—
52C23×C32#4111yescharacteristic
53C2×C32×C4C22×C411yescharacteristic
54C2×C32×C4#4111yescharacteristic
55C2×C32×C4#4112yes—
56C2×C32×C4#4112yes—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—42no—
60C2×C3×Dic3—42no—
61C32×C8—22no—
62C3⋊(C3⋊C8)—22no—
63C3×C3⋊C8—42no—
64C4×M16—91no—
65#344—32no—
66#339—92no—
67#338—91no—
68H(3,ℤ/4)—91no—
69C22×C3×C4—21no—
70C22×C3×C4C22×D312yes—
71C22×Dic3—62no—
72C22×Dic3—62no—
73C3×M16—24no—
74C3×M16—22no—
75C3×M16—22no—
76C3×M16—62no—
77C3×M16—62no—
78C2×C3×C8—22no—
79C2×C3×C8—62no—
80C2×C3×C8C4×D314yes—
81C3×C4⋊C4—62no—
82C3×C22⋊C4—62no—
83C3×C42—62no—
84#217—22no—
85C4⋊Dic3—22no—
86C4×Dic3—22no—
87C4×Dic3—32no—
88C4×Dic3—32no—
89C4×Dic3—61no—
90C4×Dic3—61no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93#208—22no—
94#208—22no—
95#208—64no—
96#208—62no—
97#208—62no—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—34no—
100C2×C3⋊C8—62no—
101C22×C32—41no—
102C22×C32#11711yescharacteristic
103C22×C32#12612yes—
104C32×C4#11711yescharacteristic
105C32×C4#11711yescharacteristic
106C32×C4#12612yes—
107C3⋊Dic3—22no—
108C3⋊Dic3—41no—
109C3×Dic3—82no—
110C2×M16—32no—
111C2×M16—91no—
112C2×M16D3211yescharacteristic
113#117—32no—
114C2×C42—91no—
115#97—92no—
116C4×C8—92no—
117C23×C3—21no—
118C23×C3#23512yes—
119C2×C3×C4—22no—
120C2×C3×C4—21no—
121C2×C3×C4—22no—
122C2×C3×C4—21no—
123C2×C3×C4—122no—
124C2×C3×C4C2×C4×D312yes—
125C2×C3×C4#23512yes—
126C2×C3×C4#23712yes—
127C2×C3×C4#23712yes—
128C2×C3×C4#23712yes—
129C2×C3×C4#23912yes—
130C2×Dic3—42no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135C2×Dic3—124no—
136C2×Dic3—124no—
137C3×C8—24no—
138C3×C8—24no—
139C3×C8—122no—
140C3⋊C8—42no—
141C3⋊C8—64no—
142C3⋊C8—64no—
143C2×C32—21no—
144C2×C32—22no—
145C2×C32#38311yescharacteristic
146C22×C4—181no—
147C22×C4C2×D3211yescharacteristic
148M16—22no—
149M16—62no—
150M16—62no—
151M16—182no—
152C2×C8—62no—
153C2×C8—92no—
154C2×C8#62412yes—
155C4⋊C4—62no—
156C22⋊C4—62no—
157C42—62no—
158C42—91no—
159C42—91no—
160C42—181no—
161C22×C3—22no—
162C22×C3—21no—
163C22×C3—42no—
164C22×C3—42no—
165C22×C3#87212yes—
166C22×C3#87912yes—
167C22×C3#89812yes—
168C3×C4—21no—
169C3×C4—22no—
170C3×C4—21no—
171C3×C4—242no—
172C3×C4#87712yes—
173C3×C4#87912yes—
174C3×C4#89212yes—
175C3×C4#89812yes—
176Dic3—64no—
177Dic3—64no—
178Dic3—82no—
179Dic3—122no—
180Dic3—122no—
181C32#184111yescharacteristic, complemented, Sylow
182C23#379811yescharacteristic
183C2×C4—122no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—362no—
187C2×C4#379612yes—
188C2×C4#379811yescharacteristic
189C2×C4#380512yes—
190C2×C4C2×#62411yescharacteristic
191C8—22no—
192C8—122no—
193C8—182no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—22no—
198C2×C3—21no—
199C2×C3—42no—
200C2×C3#465112yes—
201C22—41no—
202C22#6386212yes—
203C22#6387411yescharacteristic
204C4—182no—
205C4—242no—
206C4—361no—
207C4#6384911yescharacteristic
208C4#6386212yes—
209C4#6395711yescharacteristic
210C3—21no—
211C3#6901712yescomplemented
212C2—21no—
213C2—22no—
214C2#1059122911yescharacteristic
subgroupG/H
centerC4#63957
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#383
prime radicalC23×C32#41
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1841
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
12. #63642C4semidirect
13. C8×C3⋊Dic3C4semidirect
181. C32#1841semidirect
211. C3#69017semidirect

Maximal subgroups

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

subgroupindex
M16×C3⋊Dic32
C3×#45562
#105891602
#105891592
#105891572
#690173