Finite Group Databasebeta

← #11785355

Subgroups — #11785355

Order 1152.

841 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 841 conjugacy classes of subgroups — too many to draw. Only its 220 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
1C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#5212C212yesmaximal
3C2×#63574C212yesmaximal, complemented
4#10589163C212yesmaximal, complemented
5#69511—32nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×C3⋊(C3⋊C8)—24no—
8C22×C3⋊(C3⋊C8)C414yescomplemented
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×#217—22no—
12C2×C3×C4⋊Dic3C2214yes—
13C3×C3⋊#95—22no—
14#63574—24no—
15C23×C3⋊C8—32no—
16C23×C3⋊C8—61no—
17C3×#380—32no—
18#5212D312yes—
19C2×#808—34no—
20#4529—34no—
21C24×C32D411yescharacteristic
22C22×C32×C4—22no—
23C22×C32×C4—22no—
24C22×C32×C4C2×C412yes—
25C22×C32×C4D411yescharacteristic
26C22×C32×C4Q812yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3×Dic3—24no—
29C2×C3⋊(C3⋊C8)—22no—
30C2×C3⋊(C3⋊C8)—28no—
31C2×C3⋊(C3⋊C8)C2×C412yes—
32C2×C3⋊(C3⋊C8)C2×C412yes—
33C2×C3⋊(C3⋊C8)D414yes—
34C3×#217—44no—
35C3×C4⋊Dic3—24no—
36C3×C4⋊Dic3—24no—
37#1807—91noSylow
38C23×C3×C4—21no—
39C23×C3×C4C2×D312yes—
40C2×C3×C4⋊C4—34no—
41C2×C3×C22⋊C4—62no—
42C2×#217—22no—
43C2×C4⋊Dic3C2×D314yes—
44C22×C3⋊C8—32no—
45C22×C3⋊C8—38no—
46C22×C3⋊C8—32no—
47C22×C3⋊C8—64no—
48C22×C3⋊C8—61no—
49C22×C3⋊C8—61no—
50C22×C3⋊C8—68no—
51C22×C3⋊C8—68no—
52C3×#95—62no—
53C3⋊#95—22no—
54#808—68no—
55C23×C32—22no—
56C23×C32—22no—
57C23×C32C4⋊C412yes—
58C23×C32SD1614yes—
59C23×C32C2×D411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4—22no—
62C2×C32×C4—22no—
63C2×C32×C4—24no—
64C2×C32×C4C4⋊C412yes—
65C2×C32×C4C22×C411yescharacteristic
66C2×C32×C4C2×D412yes—
67C2×C32×C4C2×Q811yescharacteristic
68C2×C32×C4#4112yes—
69C2×C3×Dic3—44no—
70C2×C3×Dic3—44no—
71C2×C3×Dic3—44no—
72C3⋊(C3⋊C8)—22no—
73C3⋊(C3⋊C8)C22⋊C414yescomplemented
74C23×C8—91no—
75C2×#106—92no—
76#380—32no—
77#340—92no—
78C24×C3—21no—
79C24×C3#6712yes—
80C22×C3×C4—24no—
81C22×C3×C4—24no—
82C22×C3×C4—24no—
83C22×C3×C4—24no—
84C22×C3×C4—22no—
85C22×C3×C4—21no—
86C22×C3×C4—22no—
87C22×C3×C4—21no—
88C22×C3×C4—64no—
89C22×C3×C4Dic614yes—
90C22×C3×C4C4×D314yes—
91C22×C3×C4#6712yes—
92C22×C3×C4C22×D312yes—
93C22×Dic3—24no—
94C3×C4⋊C4—64no—
95C3×C4⋊C4—64no—
96C3×C22⋊C4—124no—
97#217—44no—
98C4⋊Dic3—24no—
99C4⋊Dic3—24no—
100C2×C3⋊C8—34no—
101C2×C3⋊C8—38no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—64no—
106C2×C3⋊C8—616no—
107C2×C3⋊C8—616no—
108C2×C3⋊C8—64no—
109C2×C3⋊C8—64no—
110C22×C32—22no—
111C22×C32—22no—
112C22×C32—28no—
113C22×C32#10614yescomplemented
114C22×C32C2×C4⋊C411yescharacteristic
115C22×C32#12112yes—
116C22×C32C2×SD1612yes—
117C22×C32#13512yes—
118C32×C4—22no—
119C32×C4C2×C22⋊C411yescharacteristic
120C32×C4#11711yescharacteristic
121C32×C4C22⋊Q812yes—
122C3×Dic3—84no—
123C23×C4D3211yescharacteristic
124C22×C8—91no—
125C22×C8—94no—
126C22×C8—91no—
127C22×C8—184no—
128C2×C4⋊C4—34no—
129C2×C22⋊C4—62no—
130#106—184no—
131#95—62no—
132C23×C3—24no—
133C23×C3—24no—
134C23×C3—24no—
135C23×C3—24no—
136C23×C3—24no—
137C23×C3—22no—
138C23×C3—21no—
139C23×C3Dic3⋊C414yes—
140C23×C3#21414yes—
141C23×C3#21514yes—
142C23×C3C2×#6712yes—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—28no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—28no—
150C2×C3×C4—24no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—124no—
157C2×C3×C4—124no—
158C2×C3×C4—124no—
159C2×C3×C4Dic3⋊C414yes—
160C2×C3×C4C2×Dic612yes—
161C2×C3×C4C2×C4×D312yes—
162C2×C3×C4D3×D414yes—
163C2×C3×C4#23714yes—
164C2×Dic3—44no—
165C2×Dic3—44no—
166C2×Dic3—44no—
167C3⋊C8—38no—
168C3⋊C8—64no—
169C3⋊C8—64no—
170C3⋊C8—64no—
171C2×C32—24no—
172C2×C32#38011yescharacteristic
173C2×C32C2×#10611yescharacteristic
174C2×C32#42711yescharacteristic
175C2×C32#46514yes—
176C24#62511yescharacteristic
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—64no—
180C22×C4#62412yes—
181C22×C4#62511yescharacteristic
182C22×C4#62712yes—
183C22×C4C2×D3211yescharacteristic
184C2×C8—92no—
185C2×C8—94no—
186C2×C8—92no—
187C2×C8—188no—
188C2×C8—182no—
189C4⋊C4—64no—
190C4⋊C4—64no—
191C22⋊C4—124no—
192C22×C3—24no—
193C22×C3—24no—
194C22×C3—216no—
195C22×C3—24no—
196C22×C3—24no—
197C22×C3—28no—
198C22×C3—28no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—24no—
202C22×C3—21no—
203C22×C3—22no—
204C22×C3#80818yescomplemented
205C22×C3C2×Dic3⋊C412yes—
206C22×C3C2×#21412yes—
207C22×C3#93914yes—
208C22×C3C2×#21512yes—
209C22×C3#95014yes—
210C3×C4—24no—
211C3×C4—24no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—22no—
215C3×C4—244no—
216C3×C4#87712yes—
217C3×C4#87814yes—
218C3×C4D3×C22⋊C412yes—
219Dic3—84no—
220C32#180711yescharacteristic, complemented, Sylow
221C23—22no—
222C23—22no—
223C23#371514yes—
224C23#372412yes—
225C23C2×#62511yescharacteristic
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—124no—
231C2×C4—124no—
232C2×C4—124no—
233C2×C4#372412yes—
234C2×C4#380512yes—
235C2×C4C2×#62411yescharacteristic
236C2×C4C2×#62711yescharacteristic
237C2×C4#381112yes—
238C8—94no—
239C8—182no—
240C2×C3—28no—
241C2×C3—28no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—24no—
245C2×C3—21no—
246C2×C3#494212yes—
247C2×C3C2×#80812yes—
248C2×C3#499812yes—
249C2×C3#504114yes—
250C2×C3#504814yes—
251C22—22no—
252C22—28no—
253C22—22no—
254C22#6357414yescomplemented
255C22#6382212yes—
256C22C2×#371512yes—
257C22C2×#372411yescharacteristic
258C22#6398012yes—
259C4—22no—
260C4—244no—
261C4#6395711yescharacteristic
262C4#6397411yescharacteristic
263C4#6398212yes—
264C3—21no—
265C3#6951112yescomplemented
266C2—24no—
267C2C2×#6357411yescharacteristic
268C2#1059113811yescharacteristic
269C2#1059117914yes—
270C2#1059172011yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1807
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63574C2semidirect
4. #10589163C2semidirect
8. C22×C3⋊(C3⋊C8)C4semidirect
73. C3⋊(C3⋊C8)C22⋊C4semidirect
113. C22×C32#106semidirect
204. C22×C3#808semidirect
220. C32#1807semidirect
254. C22#63574semidirect
265. C3#69511semidirect

Maximal subgroups

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

subgroupindex
C23×C3⋊(C3⋊C8)2
C3×#52122
C2×#635742
#105891632
#695113