Finite Group Databasebeta

← #11785727

Subgroups — #11785727

Order 1152.

841 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 841 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3#10589168C214yesmaximal, complemented
4#69973—32nomaximal
5C23×C32×C4C2211yescharacteristic
6C23×C3⋊Dic3C412yes—
7C2×C4⋊(C3⋊Dic3)—22no—
8C2×C4⋊(C3⋊Dic3)—22no—
9C2×C4⋊(C3⋊Dic3)C412yes—
10C2×C4⋊(C3⋊Dic3)C2212yes—
11C2×C3×#208C2214yes—
12C3×#830—22no—
13C3×#830—22no—
14C22×C4⋊Dic3—32no—
15C22×C4⋊Dic3—61no—
16C3×#407—32no—
17#5207D312yes—
18#4554—38no—
19C24×C32C2×C411yescharacteristic
20C22×C32×C4—24no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D412yes—
23C22×C32×C4D412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3—22no—
26C22×C3⋊Dic3—22no—
27C22×C3⋊Dic3—44no—
28C22×C3⋊Dic3C2×C414yes—
29C4⋊(C3⋊Dic3)—24no—
30C4⋊(C3⋊Dic3)—24no—
31C3×#208—28no—
32C2×C3×C3⋊C8—24no—
33#1821—91noSylow
34C23×C3×C4—21no—
35C23×C3×C4C2×D312yes—
36C23×Dic3—34no—
37C23×Dic3—62no—
38C2×C3×M16—34no—
39C2×C4⋊Dic3—34no—
40C2×C4⋊Dic3—34no—
41C2×C4⋊Dic3—62no—
42C2×C4⋊Dic3—62no—
43C2×C4⋊Dic3—64no—
44C2×C4⋊Dic3—64no—
45C2×C4⋊Dic3—62no—
46C2×C4⋊Dic3—62no—
47C2×C4⋊Dic3—62no—
48C2×C4⋊Dic3—62no—
49C2×#208C2×D314yes—
50C3×C22⋊C8—62no—
51C3×C22⋊C8—62no—
52#830—22no—
53#830—22no—
54C23×C32—22no—
55C23×C32—22no—
56C23×C32—22no—
57C23×C32C22⋊C411yescharacteristic
58C23×C32C22⋊C411yescharacteristic
59C23×C32C22×C411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4—24no—
62C2×C32×C4—24no—
63C2×C32×C4C22⋊C412yes—
64C2×C32×C4C2×D412yes—
65C2×C32×C4#4114yes—
66C2×C3⋊Dic3—24no—
67C2×C3⋊Dic3—44no—
68C2×C3⋊Dic3—44no—
69C2×C3⋊Dic3—44no—
70C3×C3⋊C8—44no—
71C22×C4⋊C4—91no—
72#407—32no—
73#343—94no—
74C24×C3—21no—
75C24×C3C4×D312yes—
76C22×C3×C4—28no—
77C22×C3×C4—28no—
78C22×C3×C4—21no—
79C22×C3×C4—22no—
80C22×C3×C4—22no—
81C22×C3×C4—21no—
82C22×C3×C4C4×D312yes—
83C22×C3×C4D1212yes—
84C22×C3×C4D1212yes—
85C22×C3×C4#6712yes—
86C22×C3×C4#6712yes—
87C22×C3×C4C22×D312yes—
88C22×Dic3—38no—
89C22×Dic3—64no—
90C22×Dic3—64no—
91C22×Dic3—64no—
92C22×Dic3—64no—
93C22×Dic3—64no—
94C22×Dic3—128no—
95C22×Dic3—128no—
96C3×M16—68no—
97C2×C3×C8—64no—
98C4⋊Dic3—68no—
99C4⋊Dic3—68no—
100C4⋊Dic3—64no—
101C4⋊Dic3—64no—
102C4⋊Dic3—64no—
103C4⋊Dic3—64no—
104#208—28no—
105C2×C3⋊C8—24no—
106C22×C32—28no—
107C22×C32—21no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32#10012yes—
114C22×C32#10112yes—
115C22×C32C2×C22⋊C411yescharacteristic
116C22×C32#11712yes—
117C32×C4—22no—
118C32×C4#12314yes—
119C3⋊Dic3—44no—
120C23×C4—92no—
121C23×C4D3211yescharacteristic
122C2×M16—34no—
123C2×C4⋊C4—92no—
124C2×C4⋊C4—92no—
125C2×C4⋊C4—182no—
126C2×C4⋊C4—182no—
127C22⋊C8—62no—
128C22⋊C8—62no—
129C23×C3—24no—
130C23×C3—24no—
131C23×C3—24no—
132C23×C3—24no—
133C23×C3—24no—
134C23×C3—24no—
135C23×C3—21no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3(C2×D3)⋊C412yes—
139C23×C3(C2×D3)⋊C412yes—
140C23×C3C2×C4×D312yes—
141C2×C3×C4—24no—
142C2×C3×C4—28no—
143C2×C3×C4—28no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—22no—
150C2×C3×C4—24no—
151C2×C3×C4—22no—
152C2×C3×C4(C2×D3)⋊C412yes—
153C2×C3×C4(C2×D3)⋊C412yes—
154C2×C3×C4C2×D1212yes—
155C2×C3×C4#23718yes—
156C2×C3×C4C2×#6712yes—
157C2×Dic3—68no—
158C2×Dic3—68no—
159C2×Dic3—128no—
160C2×Dic3—128no—
161C2×Dic3—128no—
162C2×Dic3—128no—
163C2×Dic3—128no—
164C2×Dic3—128no—
165C3×C8—124no—
166C3⋊C8—44no—
167C2×C32—22no—
168C2×C32—22no—
169C2×C32—22no—
170C2×C32#38111yescharacteristic
171C2×C32C2×#10011yescharacteristic
172C2×C32C2×#10111yescharacteristic
173C24#62411yescharacteristic
174C22×C4—24no—
175C22×C4—94no—
176C22×C4—182no—
177C22×C4—182no—
178C22×C4—364no—
179C22×C4#62411yescharacteristic
180C22×C4#62612yes—
181C22×C4#62612yes—
182C22×C4C2×D3211yescharacteristic
183M16—68no—
184C2×C8—64no—
185C4⋊C4—184no—
186C4⋊C4—184no—
187C22×C3—22no—
188C22×C3—22no—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—216no—
192C22×C3—216no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—21no—
205C22×C3#82314yes—
206C22×C3#82414yes—
207C22×C3#87714yes—
208C22×C3C2×(C2×D3)⋊C412yes—
209C3×C4—24no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—24no—
213C3×C4#88614yes—
214C3×C4#93514yes—
215Dic3—128no—
216Dic3—128no—
217C32#182111yescharacteristic, complemented, Sylow
218C23—22no—
219C23—22no—
220C23—22no—
221C23#372211yescharacteristic
222C23#372211yescharacteristic
223C23C2×#62411yescharacteristic
224C2×C4—22no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—184no—
228C2×C4—364no—
229C2×C4—364no—
230C2×C4—364no—
231C2×C4#372212yes—
232C2×C4#380514yes—
233C2×C4C2×#62612yes—
234C8—124no—
235C2×C3—24no—
236C2×C3—24no—
237C2×C3—24no—
238C2×C3—24no—
239C2×C3—24no—
240C2×C3—24no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3#494312yes—
245C2×C3C2×#82312yes—
246C2×C3C2×#82412yes—
247C22—28no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22#6355912yes—
255C22#6356112yes—
256C22#6395712yes—
257C22C2×#372211yescharacteristic
258C4—22no—
259C4—364no—
260C4#6396214yes—
261C3—21no—
262C3#6997312yescomplemented
263C2—22no—
264C2—22no—
265C2—22no—
266C2C2×#6355911yescharacteristic
267C2C2×#6356111yescharacteristic
268C2#1059169711yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1821
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10589168C2semidirect
217. C32#1821semidirect
262. C3#69973semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C3×#52072
#105891682
#699733