Finite Group Databasebeta

← #11784199

Subgroups — #11784199

Order 1152.

713 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 212 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
1C42×C3⋊Dic3C211yesmaximal, characteristic
2C2×#63572C212yesmaximal
3C2×#63555C212yesmaximal
4C3×#4524C212yesmaximal
5#68603—32nomaximal
6C2×C32×C42C2211yescharacteristic
7C2×C4×C3⋊Dic3C412yes—
8C2×C4×C3⋊Dic3C412yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3×C3⋊C8C2214yes—
12#63572C418yescomplemented
13#63555—24no—
14C2×#815—34no—
15C2×Dic3⋊C8—34no—
16C42×Dic3—32no—
17C42×Dic3—61no—
18C3×#336—32no—
19#4524D312yes—
20C22×C32×C4C2×C412yes—
21C22×C32×C4C2311yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C412yes—
24C22×C3⋊Dic3C2×C411yescharacteristic
25C32×C42—22no—
26C4×C3⋊Dic3—24no—
27C4×C3⋊Dic3—24no—
28C4×C3⋊Dic3C2×C414yes—
29C4×C3⋊Dic3D412yes—
30C4×C3⋊Dic3Q812yes—
31C2×C3×C3⋊C8—24no—
32C2×C3×C3⋊C8—24no—
33C2×C3×C3⋊C8C2×C418yes—
34#1767—91noSylow
35C22×C3×C8—34no—
36C2×C3×C42—21no—
37C2×C3×C42C2×D312yes—
38C2×C4×Dic3—32no—
39C2×C4×Dic3—32no—
40C2×C4×Dic3—34no—
41C2×C4×Dic3—34no—
42C2×C4×Dic3—62no—
43C2×C4×Dic3—62no—
44C2×C4×Dic3—61no—
45C2×C4×Dic3—61no—
46C22×C3⋊C8C2×D314yes—
47#815—68no—
48Dic3⋊C8—316no—
49C23×C32C22×C411yescharacteristic
50C2×C32×C4—22no—
51C2×C32×C4—22no—
52C2×C32×C4M1614yes—
53C2×C32×C4C22×C412yes—
54C2×C32×C4C2×D411yescharacteristic
55C2×C32×C4C2×Q811yescharacteristic
56C2×C32×C4#4112yes—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3C4212yes—
61C2×C3⋊Dic3C4212yes—
62C2×C3⋊Dic3C4⋊C414yes—
63C2×C3⋊Dic3M1614yes—
64C3×C3⋊C8—28no—
65C2×C4⋊C8—92no—
66C2×#97—92no—
67C43—91no—
68#336—32no—
69C22×C3×C4—22no—
70C22×C3×C4—21no—
71C22×C3×C4C4×D314yes—
72C22×C3×C4C22×D312yes—
73C22×Dic3—32no—
74C22×Dic3—32no—
75C22×Dic3—34no—
76C22×Dic3—61no—
77C22×Dic3—61no—
78C22×Dic3—62no—
79C2×C3×C8—38no—
80C2×C3×C8—64no—
81C2×C3×C8—64no—
82C3×C42—24no—
83C3×C42—24no—
84C4×Dic3—38no—
85C4×Dic3—34no—
86C4×Dic3—34no—
87C4×Dic3—64no—
88C4×Dic3—62no—
89C4×Dic3—62no—
90C4×Dic3—68no—
91C4×Dic3—68no—
92C4×Dic3—68no—
93C4×Dic3—68no—
94C2×C3⋊C8—24no—
95C2×C3⋊C8—24no—
96C2×C3⋊C8C4×D318yes—
97C22×C32C2×C4211yescharacteristic
98C22×C32C2×C4⋊C411yescharacteristic
99C22×C32#11711yescharacteristic
100C22×C32C2×M1612yes—
101C22×C32C2×M1612yes—
102C32×C4—24no—
103C32×C4C4×D412yes—
104C32×C4C4×Q812yes—
105C3⋊Dic3—22no—
106C3⋊Dic3—24no—
107C3⋊Dic3#9714yescomplemented
108C22×C8—34no—
109C2×C42—91no—
110C2×C42—91no—
111C2×C42—92no—
112C2×C42—92no—
113C2×C42D3211yescharacteristic
114C4⋊C8—98no—
115#97—184no—
116C23×C3—21no—
117C23×C3C2×C4×D312yes—
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×C3×C4—24no—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—21no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—22no—
127C2×C3×C4ΓL(1,𝔽25)18yes—
128C2×C3×C4C2×C4×D314yes—
129C2×C3×C4D3×D412yes—
130C2×C3×C4#23714yes—
131C2×C3×C4D3×Q812yes—
132C2×Dic3—34no—
133C2×Dic3—38no—
134C2×Dic3—34no—
135C2×Dic3—38no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—64no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—64no—
144C2×Dic3—64no—
145C2×Dic3—64no—
146C3×C8—68no—
147C3⋊C8—28no—
148C2×C32C4×C4⋊C411yescharacteristic
149C2×C32C2×#9711yescharacteristic
150C2×C32C4×M1611yescharacteristic
151C2×C32#42312yes—
152C2×C32#43212yes—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—92no—
156C22×C4#62412yes—
157C22×C4C2×D3211yescharacteristic
158C2×C8—38no—
159C2×C8—64no—
160C2×C8—64no—
161C42—22no—
162C42—92no—
163C42—94no—
164C42—92no—
165C42—184no—
166C42—184no—
167C22×C3—22no—
168C22×C3—22no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3C42×D312yes—
173C22×C3#87712yes—
174C22×C3D3×C4⋊C412yes—
175C22×C3C2×ΓL(1,𝔽25)14yes—
176C22×C3D3×M1614yes—
177C3×C4—28no—
178C3×C4—28no—
179C3×C4—22no—
180C3×C4—22no—
181C3×C4#67⋊C414yes—
182C3×C4#88714yes—
183Dic3—38no—
184Dic3—64no—
185Dic3—64no—
186Dic3—68no—
187Dic3—64no—
188Dic3—68no—
189C32#176711yescharacteristic, complemented, Sylow
190C23C2×#62411yescharacteristic
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—94no—
194C2×C4—92no—
195C2×C4—92no—
196C2×C4—94no—
197C2×C4—182no—
198C2×C4—182no—
199C2×C4—182no—
200C2×C4#371214yes—
201C2×C4#379711yescharacteristic
202C2×C4C4×D3212yes—
203C2×C4#380211yescharacteristic
204C2×C4#380512yes—
205C8—68no—
206C2×C3—21no—
207C2×C3—22no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—22no—
211C2×C3#464912yes—
212C2×C3C4×ΓL(1,𝔽25)12yes—
213C2×C3D3×#9712yes—
214C2×C3#471914yes—
215C2×C3#483714yes—
216C22#6381812yes—
217C22C2×#371212yes—
218C22C4×#62411yescharacteristic
219C22#6390011yescharacteristic
220C22#6395711yescharacteristic
221C4—24no—
222C4—94no—
223C4—182no—
224C4—184no—
225C4#6383812yes—
226C4#6390212yes—
227C3—21no—
228C3#6860312yescomplemented
229C2#1059032211yescharacteristic
230C2C4×#371211yescharacteristic
231C2#1059034012yes—
232C2#1059106612yes—
233C2#1059125711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC2×C32×C42C22
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1767
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
12. #63572C4semidirect
107. C3⋊Dic3#97semidirect
189. C32#1767semidirect
228. C3#68603semidirect

Maximal subgroups

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

subgroupindex
C42×C3⋊Dic32
C2×#635722
C2×#635552
C3×#45242
#686033