Finite Group Databasebeta

← #11771741

Subgroups — #11771741

Order 1152.

237 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 237 conjugacy classes of subgroups — too many to draw. Only its 58 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×#5137C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic
3C3×#4557C211yesmaximal, characteristic
4#67780—31nomaximal
5#67482—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C3×#926—21no—
8C3×#924—21no—
9C2×C3×Dic12C411yescharacteristic, complemented
10#63639—21no—
11C3×#817C411yescharacteristic, complemented
12C3×#816—21no—
13C3×#470—31no—
14#5137D311yescharacteristic
15C3×H(3,ℤ/4)—31no—
16#4557D311yescharacteristic
17#4553—31no—
18#4553—31no—
19#4553—61no—
20C22×C32×C4D411yescharacteristic
21C2×C3×Dic6—21no—
22C32×M16—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C32×C8D411yescharacteristic
25C3×#217—41no—
26C3×#217—41no—
27C3×C4⋊Dic3—21no—
28C3×C4⋊Dic3—41no—
29C3×Dic3⋊C4—41no—
30C3×C4×Dic3—22no—
31C3×Dic12—41no—
32C3⋊(C3⋊C16)—41no—
33#1340—91noSylow
34C2×C3×Q16—31no—
35C2×C3×M16—21no—
36C2×C3×M16C2×D311yescharacteristic
37C2×C3×M16C2×D311yescharacteristic
38C3×C22⋊Q8—61no—
39C3×#117—61no—
40#926—21no—
41#924—21no—
42C2×Dic12Dic311yescharacteristic, complemented
43C3×#106—31no—
44C3×#103—61no—
45#817Dic311yescharacteristic, complemented
46#816—21no—
47#812—62no—
48#812—61no—
49#812—61no—
50C23×C32D811yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4SD1611yescharacteristic
55C2×C3×Dic3—42no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58C3×Dic6—41no—
59C3×Dic6—41no—
60C32×C8—21no—
61C32×C8—21no—
62#470—31no—
63#349—91no—
64H(3,ℤ/4)—31no—
65C2×C3×Q8—61no—
66C22×C3×C4—21no—
67C22×C3×C4#6711yescharacteristic
68C22×C3×C4#6711yescharacteristic
69C2×Dic6—21no—
70C3×Q16—121no—
71C3×M16—41no—
72C3×M16—41no—
73C3×M16—42no—
74C2×C3×C8—21no—
75C2×C3×C8—21no—
76C2×C3×C8C4×D311yescharacteristic
77C2×C3×C8D1211yescharacteristic
78C2×C3×C8C2×Dic311yescharacteristic
79C2×C3×C8#6711yescharacteristic
80C3×C4⋊C4—61no—
81C3×C4⋊C4—121no—
82C3×C4⋊C4—121no—
83C3×C22⋊C4—121no—
84C3×C22⋊C4—121no—
85C3×C42—62no—
86#217—41no—
87#217—41no—
88C4⋊Dic3—21no—
89C4⋊Dic3—41no—
90Dic3⋊C4—41no—
91C4×Dic3—22no—
92Dic12—41no—
93C3⋊C16—122no—
94C3⋊C16—121no—
95C3⋊C16—121no—
96C22×C32—21no—
97C22×C32—41no—
98C22×C32#10211yescharacteristic
99C32×C4—21no—
100C32×C4#9911yescharacteristic
101C32×C4#10411yescharacteristic
102C3×Dic3—81no—
103C3×Dic3—82no—
104C3×Dic3—81no—
105C2×Q16—31no—
106C2×M16D3211yescharacteristic
107C22⋊Q8—61no—
108#117—61no—
109M32—181no—
110#106—31no—
111#103—61no—
112C23×C3—21no—
113C23×C3#21311yescharacteristic
114C23×C3#21311yescharacteristic
115C3×Q8—121no—
116C3×Q8—121no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—41no—
124C2×C3×C4—41no—
125C2×C3×C4—122no—
126C2×C3×C4—121no—
127C2×C3×C4—121no—
128C2×C3×C4(C2×D3)⋊C411yescharacteristic
129C2×C3×C4#21411yescharacteristic
130C2×C3×C4#21511yescharacteristic
131C2×C3×C4#21711yescharacteristic
132C2×Dic3—42no—
133C2×Dic3—41no—
134C2×Dic3—41no—
135Dic6—41no—
136Dic6—41no—
137C3×C8—22no—
138C3×C8—21no—
139C3×C8—21no—
140C3×C8—21no—
141C3×C8—21no—
142C3×C8—41no—
143C2×C32—21no—
144C2×C32—41no—
145C2×C32#32711yescharacteristic
146C2×Q8—61no—
147C22×C4#62511yescharacteristic
148Q16—121no—
149M16—41no—
150C2×C8D3×Dic311yescharacteristic
151C2×C8#62611yescharacteristic
152C4⋊C4—61no—
153C4⋊C4—121no—
154C4⋊C4—121no—
155C22⋊C4—121no—
156C22⋊C4—121no—
157C42—62no—
158C16—361no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—21no—
162C22×C3—41no—
163C22×C3—41no—
164C22×C3—41no—
165C22×C3—81no—
166C22×C3#80911yescharacteristic
167C22×C3#83211yescharacteristic
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—241no—
174C3×C4—242no—
175C3×C4—241no—
176C3×C4#80511yescharacteristic
177C3×C4#80611yescharacteristic
178C3×C4#83411yescharacteristic
179C3×C4#83711yescharacteristic
180Dic3—81no—
181Dic3—82no—
182Dic3—81no—
183C32#134011yescharacteristic, complemented, Sylow
184C23#371311yescharacteristic
185Q8—121no—
186Q8—121no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—122no—
190C2×C4—121no—
191C2×C4—121no—
192C2×C4#371511yescharacteristic
193C2×C4(C2×D3)⋊Dic311yescharacteristic
194C8—21no—
195C8—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—41no—
200C2×C3—41no—
201C2×C3—41no—
202C2×C3—81no—
203C2×C3#445111yescharacteristic
204C2×C3#453711yescharacteristic
205C22—21no—
206C22—41no—
207C22#6356211yescharacteristic
208C4—21no—
209C4—241no—
210C4—242no—
211C4—241no—
212C4#6356911yescharacteristic
213C4#6358011yescharacteristic
214C3—21no—
215C3#6748211yescharacteristic, complemented
216C3#6778011yescharacteristic, complemented
217C2—21no—
218C2—41no—
219C2#1058914911yescharacteristic
subgroupG/H
centerC2#10589149
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#327
prime radicalC23×C32D8
hypocenterC32#1340
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
9. C2×C3×Dic12C4semidirect
11. C3×#817C4semidirect
42. C2×Dic12Dic3semidirect
45. #817Dic3semidirect
183. C32#1340semidirect
215. C3#67482semidirect
216. C3#67780semidirect

Maximal subgroups

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

subgroupindex
C3×#51372
#105894192
C3×#45572
#677803
#674823