Finite Group Databasebeta

← #11790498

Subgroups — #11790498

Order 1152.

457 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 457 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#10592696C211yesmaximal, characteristic
2C3×#4995C212yesmaximal
3C2×#63578C211yesmaximal, characteristic
4C2×#63576C211yesmaximal, characteristic
5#10589167C212yesmaximal
6#70669—32nomaximal
7C32×#117C2211yescharacteristic
8C2×#3748C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12#63630—21no—
13C4×C3⋊(C3⋊C8)—21no—
14C3×#808—22no—
15C3×#807—22no—
16#63578C414yescomplemented
17#63576—21no—
18#63576—21no—
19C3×#428—32no—
20C2×#822—32no—
21#4997—32no—
22#4997—61no—
23#4995D312yes—
24C2×#807—32no—
25#4554—32no—
26#4530—32no—
27C22×C32×C4C2311yescharacteristic
28C22×C3×Dic3—22no—
29C32×C4⋊C4D411yescharacteristic
30C32×C4⋊C4D411yescharacteristic
31C32×C22⋊C4—21no—
32C32×C42—21no—
33#3748—21no—
34#3748Q812yes—
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3⋊(C3⋊C8)C2×C412yes—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C2×C3⋊(C3⋊C8)Q812yes—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×#208—22no—
43C3×#208C2×C414yes—
44C2×C3×C3⋊C8—22no—
45#1952—91noSylow
46C2×C3×M16—32no—
47C3×#117—21no—
48C3×#117C2×D312yes—
49C2×C3×C4⋊C4—32no—
50C2×C4⋊Dic3C2×D312yes—
51C2×#208—32no—
52C2×#208—61no—
53C2×#208C2×D312yes—
54C22×C3⋊C8—32no—
55C22×C3⋊C8—61no—
56C3×#107—62no—
57C3×#106—62no—
58#822—38no—
59#808—22no—
60#807—22no—
61#807—62no—
62#807—62no—
63#803—62no—
64#803—62no—
65C4×C3⋊C8—62no—
66C4×C3⋊C8—62no—
67C23×C32#4111yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4C22×C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×Q811yescharacteristic
74C2×C32×C4C2×Q811yescharacteristic
75C2×C32×C4#4111yescharacteristic
76C2×C3×Dic3—42no—
77C2×C3×Dic3—82no—
78C3⋊(C3⋊C8)—22no—
79C3⋊(C3⋊C8)C4⋊C412yes—
80C3⋊(C3⋊C8)C4⋊C412yes—
81C3×C3⋊C8—24no—
82C2×#108—91no—
83#428—32no—
84C2×#107—91no—
85#405—91no—
86#343—92no—
87C22×C3×C4—21no—
88C22×C3×C4—62no—
89C22×C3×C4C22×D312yes—
90C22×Dic3—22no—
91C3×M16—34no—
92C3×M16—62no—
93C2×C3×C8—62no—
94C3×C4⋊C4—21no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4—62no—
97C3×C4⋊C4—62no—
98C3×C4⋊C4#6712yes—
99C3×C4⋊C4#6712yes—
100C3×C22⋊C4—22no—
101C3×C22⋊C4—22no—
102C3×C42—22no—
103C3×C42—22no—
104C4⋊Dic3—22no—
105C4⋊Dic3—22no—
106#208—22no—
107#208—34no—
108#208—62no—
109#208—62no—
110#208—62no—
111#208C4×D314yes—
112C2×C3⋊C8—22no—
113C2×C3⋊C8—34no—
114C2×C3⋊C8—32no—
115C2×C3⋊C8—32no—
116C2×C3⋊C8—34no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8—61no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—62no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32C4×Q811yescharacteristic
126C22×C32#12111yescharacteristic
127C22×C32#12511yescharacteristic
128C32×C4—41no—
129C32×C4—41no—
130C32×C4C2×C4⋊C411yescharacteristic
131C32×C4C4×D411yescharacteristic
132C32×C4C22⋊Q811yescharacteristic
133C32×C4C4⋊Q811yescharacteristic
134C3×Dic3—82no—
135C2×M16—32no—
136C2×M16—91no—
137C22×C8—91no—
138#117D3211yescharacteristic
139C2×C4⋊C4—32no—
140#108—94no—
141#107—62no—
142#107—181no—
143#107—181no—
144#106—62no—
145#97—181no—
146C4×C8—181no—
147C23×C3—21no—
148C23×C3#23712yes—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—122no—
160C2×C3×C4—242no—
161C2×C3×C4C2×C4×D312yes—
162C2×C3×C4#23512yes—
163C2×C3×C4D3×D412yes—
164C2×C3×C4D3×Q812yes—
165C2×C3×C4D3×Q812yes—
166C2×C3×C4C2×#6712yes—
167C2×Dic3—42no—
168C2×Dic3—82no—
169C3×C8—64no—
170C3⋊C8—24no—
171C3⋊C8—34no—
172C3⋊C8—34no—
173C3⋊C8—62no—
174C3⋊C8—62no—
175C3⋊C8—64no—
176C3⋊C8—64no—
177C2×C32—21no—
178C2×C32—21no—
179C2×C32#38911yescharacteristic
180C2×C32#47211yescharacteristic
181C2×C32#47311yescharacteristic
182C22×C4—62no—
183C22×C4C2×D3211yescharacteristic
184M16—34no—
185M16—62no—
186M16—92no—
187M16—181no—
188C2×C8—62no—
189C2×C8—92no—
190C2×C8—92no—
191C2×C8—91no—
192C2×C8—91no—
193C2×C8—181no—
194C4⋊C4—62no—
195C4⋊C4—62no—
196C4⋊C4#62511yescharacteristic
197C4⋊C4#62511yescharacteristic
198C22⋊C4—21no—
199C42—21no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—41no—
206C22×C3—41no—
207C22×C3#88712yes—
208C22×C3#88912yes—
209C22×C3#93912yes—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—42no—
215C3×C4—42no—
216C3×C4—42no—
217C3×C4—42no—
218C3×C4—242no—
219C3×C4D3×C4⋊C412yes—
220C3×C4#89612yes—
221C3×C4C4×#6712yes—
222C3×C4#94412yes—
223Dic3—82no—
224C32#195211yescharacteristic, complemented, Sylow
225C23#380511yescharacteristic
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—122no—
229C2×C4—242no—
230C2×C4#379711yescharacteristic
231C2×C4#379711yescharacteristic
232C2×C4#379811yescharacteristic
233C2×C4C4×D3211yescharacteristic
234C2×C4C2×#62511yescharacteristic
235C2×C4#381111yescharacteristic
236C8—64no—
237C8—92no—
238C8—92no—
239C8—182no—
240C2×C3—22no—
241C2×C3—22no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—41no—
246C2×C3—41no—
247C2×C3#497612yes—
248C2×C3#519912yes—
249C2×C3#520412yes—
250C22—21no—
251C22—21no—
252C22#6383811yescharacteristic
253C22#6387011yescharacteristic
254C22#6398011yescharacteristic
255C4—41no—
256C4—41no—
257C4—242no—
258C4#6386511yescharacteristic
259C4#6387311yescharacteristic
260C4#6388311yescharacteristic
261C4C4×#62511yescharacteristic
262C3—21no—
263C3#7066912yescomplemented
264C2—21no—
265C2—21no—
266C2#1059133711yescharacteristic
267C2#1059167811yescharacteristic
268C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC23×C32#41
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1952
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
16. #63578C4semidirect
224. C32#1952semidirect
263. C3#70669semidirect

Maximal subgroups

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

subgroupindex
#105926962
C3×#49952
C2×#635782
C2×#635762
#105891672
#706693