Finite Group Databasebeta

← #11786232

Subgroups — #11786232

Order 1152.

653 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 202 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#10592674C211yesmaximal, characteristic
2C2×C3×#807C212yesmaximal
3#10591359C211yesmaximal, characteristic
4C2×#63575C212yesmaximal
5C2×#63553C211yesmaximal, characteristic
6#70606—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×#3750—22no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—22no—
14C3×#807—24no—
15#63575—24no—
16#63553C414yescomplemented
17C2×C3×#107—32no—
18C2×#818—32no—
19C2×C8×Dic3—32no—
20#4975—32no—
21#4975—32no—
22#4975—61no—
23C2×#807—32no—
24C2×#807D312yes—
25C22×C32×C4—21no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3D412yes—
29C22×C3×Dic3—22no—
30C32×C4⋊C4—22no—
31C4⋊(C3⋊Dic3)—22no—
32#3750—44no—
33C4×C3⋊Dic3C2×C412yes—
34C4×C3⋊Dic3Q812yes—
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8C2×C414yes—
38C2×C3×C3⋊C8D414yes—
39C2×C3×C3⋊C8Q814yes—
40#3724—44no—
41#1845—91noSylow
42C22×C3×C8—32no—
43C2×C3×C4⋊C4—21no—
44C2×C3×C4⋊C4—32no—
45C2×C3×C4⋊C4C2×D312yes—
46C2×C4⋊Dic3—32no—
47C2×C4⋊Dic3—61no—
48C2×C4⋊Dic3C2×D312yes—
49C2×Dic3⋊C4—64no—
50C2×Dic3⋊C4—64no—
51C2×Dic3⋊C4—64no—
52C2×C4×Dic3—32no—
53C2×C4×Dic3—61no—
54C22×C3⋊C8C2×D312yes—
55C3×#107—64no—
56#818—64no—
57C8×Dic3—38no—
58#807—24no—
59#807—64no—
60C23×C32C2×D411yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4—42no—
63C2×C32×C4C22×C411yescharacteristic
64C2×C32×C4C2×D412yes—
65C2×C32×C4C2×Q812yes—
66C2×C32×C4C2×Q811yescharacteristic
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—42no—
69C2×C3⋊Dic3C4⋊C414yes—
70C2×C3⋊Dic3D814yes—
71C2×C3⋊Dic3Q1614yes—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—44no—
74C3×C3⋊C8C4⋊C418yescomplemented
75C2×#107—32no—
76C2×#107—92no—
77C2×C4×C8—91no—
78#384—91no—
79#384—91no—
80C22×C3×C4—22no—
81C22×C3×C4—22no—
82C22×C3×C4—21no—
83C22×C3×C4—62no—
84C22×C3×C4C22×D312yes—
85C22×Dic3—22no—
86C22×Dic3—34no—
87C22×Dic3—62no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C2×C3×C8—34no—
91C2×C3×C8—34no—
92C2×C3×C8—34no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—42no—
96C3×C4⋊C4—62no—
97C3×C4⋊C4—62no—
98C4⋊Dic3—22no—
99C4⋊Dic3—22no—
100C4⋊Dic3—62no—
101C4⋊Dic3—62no—
102C4⋊Dic3—122no—
103Dic3⋊C4—128no—
104Dic3⋊C4—128no—
105Dic3⋊C4—128no—
106C4×Dic3—34no—
107C4×Dic3—34no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C2×C3⋊C8Dic614yes—
111C2×C3⋊C8C4×D314yes—
112C2×C3⋊C8#6714yes—
113C22×C32C2×C4⋊C411yescharacteristic
114C22×C32#12711yescharacteristic
115C22×C32C4⋊Q811yescharacteristic
116C22×C32C2×D812yes—
117C22×C32C2×Q1612yes—
118C32×C4—81no—
119C32×C4C2×C4⋊C412yes—
120C32×C4C4⋊Q812yes—
121C3⋊Dic3—81no—
122C3⋊Dic3#10718yescomplemented
123C3×Dic3—82no—
124C22×C8—32no—
125C2×C4⋊C4—32no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4—182no—
128C2×C4⋊C4—182no—
129C2×C4⋊C4D3211yescharacteristic
130C2×C42—91no—
131#107—64no—
132#107—184no—
133C4×C8—94no—
134C23×C3—21no—
135C23×C3D3×D412yes—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—22no—
140C2×C3×C4—44no—
141C2×C3×C4—42no—
142C2×C3×C4—44no—
143C2×C3×C4—42no—
144C2×C3×C4—124no—
145C2×C3×C4—122no—
146C2×C3×C4C2×Dic612yes—
147C2×C3×C4C2×C4×D312yes—
148C2×C3×C4D3×D412yes—
149C2×C3×C4D3×Q812yes—
150C2×C3×C4D3×Q812yes—
151C2×C3×C4C2×#6712yes—
152C2×Dic3—38no—
153C2×Dic3—38no—
154C2×Dic3—38no—
155C2×Dic3—44no—
156C2×Dic3—42no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—124no—
161C2×Dic3—122no—
162C2×Dic3—124no—
163C2×Dic3—122no—
164C3×C8—38no—
165C3⋊C8Dic3⋊C418yescomplemented
166C2×C32#38411yescharacteristic
167C2×C32C2×#10712yes—
168C2×C32#49311yescharacteristic
169C2×C32#49411yescharacteristic
170C2×C32#50012yes—
171C22×C4—21no—
172C22×C4—62no—
173C22×C4—92no—
174C22×C4—181no—
175C22×C4C2×D3211yescharacteristic
176C2×C8—34no—
177C2×C8—34no—
178C2×C8—34no—
179C4⋊C4—22no—
180C4⋊C4—62no—
181C4⋊C4—62no—
182C4⋊C4—182no—
183C4⋊C4—364no—
184C4⋊C4—364no—
185C42—92no—
186C42—92no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—21no—
192C22×C3#88812yes—
193C22×C3D3×C4⋊C412yes—
194C22×C3D3×D814yes—
195C22×C3D3×Q1614yes—
196C22×C3#94012yes—
197C3×C4—22no—
198C3×C4—22no—
199C3×C4—82no—
200C3×C4—82no—
201C3×C4—242no—
202C3×C4#88812yes—
203C3×C4D3×C4⋊C412yes—
204C3×C4C2×Dic3⋊C412yes—
205C3×C4#94412yes—
206Dic3—316no—
207Dic3—68no—
208Dic3—82no—
209Dic3—242no—
210Dic3—242no—
211C32#184511yescharacteristic, complemented, Sylow
212C23#381111yescharacteristic
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—94no—
216C2×C4—94no—
217C2×C4—94no—
218C2×C4—124no—
219C2×C4—122no—
220C2×C4—362no—
221C2×C4—361no—
222C2×C4D3×Dic612yes—
223C2×C4#379711yescharacteristic
224C2×C4C4×D3211yescharacteristic
225C2×C4D3×#6712yes—
226C8—38no—
227C2×C3—21no—
228C2×C3—22no—
229C2×C3—21no—
230C2×C3—22no—
231C2×C3—21no—
232C2×C3#487414yes—
233C2×C3D3×#10714yes—
234C2×C3#497512yes—
235C2×C3#515112yes—
236C2×C3#518312yes—
237C22#6384011yescharacteristic
238C22#6388311yescharacteristic
239C22#6392612yes—
240C22#6394412yes—
241C22#6397911yescharacteristic
242C4—81no—
243C4—98no—
244C4—242no—
245C4—721no—
246C4#6383912yes—
247C4D3×Dic3⋊C412yes—
248C3—21no—
249C3#7060612yescomplemented
250C2#1059041512yes—
251C2#1059057312yes—
252C2#1059124411yescharacteristic
253C2#1059148411yescharacteristic
254C2#1059162811yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1845
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #63553C4semidirect
74. C3×C3⋊C8C4⋊C4semidirect
122. C3⋊Dic3#107semidirect
165. C3⋊C8Dic3⋊C4semidirect
211. C32#1845semidirect
249. C3#70606semidirect

Maximal subgroups

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

subgroupindex
#105926742
C2×C3×#8072
#105913592
C2×#635752
C2×#635532
#706063