Finite Group Databasebeta

← #11786054

Subgroups — #11786054

Order 1152.

509 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 154 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#10592676C211yesmaximal, characteristic
2#10591230C211yesmaximal, characteristic
3C2×#63553C211yesmaximal, characteristic
4C3×#4529C212yesmaximal
5#10589164C212yesmaximal
6#68848—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12#63658—22no—
13#63579—22no—
14#63553C414yescomplemented
15C2×C8×Dic3—32no—
16#4977—32no—
17#4977—32no—
18#4977—61no—
19C3×#340—32no—
20#4551—32no—
21#4529—32no—
22#4529D312yes—
23C22×C32×C4—21no—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3D412yes—
27C22×C3×Dic3—22no—
28C32×C4⋊C4—22no—
29C4⋊(C3⋊Dic3)—22no—
30C4×C3⋊Dic3C2×C412yes—
31C4×C3⋊Dic3Q812yes—
32C3×C4⋊Dic3—22no—
33C3×C4⋊Dic3—22no—
34C2×C3×C3⋊C8—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8C2×C414yes—
37#1835—91noSylow
38C22×C3×C8—32no—
39C2×C3×C4⋊C4—21no—
40C2×C3×C4⋊C4—32no—
41C2×C3×C4⋊C4C2×D312yes—
42C2×C4⋊Dic3—32no—
43C2×C4⋊Dic3—61no—
44C2×C4⋊Dic3C2×D312yes—
45C2×C4×Dic3—32no—
46C2×C4×Dic3—61no—
47C22×C3⋊C8C2×D312yes—
48C3⋊#95—62no—
49C3⋊#95—62no—
50C3⋊#95—62no—
51C3⋊#95—62no—
52C3⋊#95—64no—
53C8×Dic3—38no—
54C23×C32C2×D411yescharacteristic
55C2×C32×C4—41no—
56C2×C32×C4—42no—
57C2×C32×C4C22×C411yescharacteristic
58C2×C32×C4C2×Q811yescharacteristic
59C2×C32×C4#4112yes—
60C2×C32×C4#4112yes—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—42no—
65C2×C3⋊Dic3C4⋊C414yes—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68C2×C3×Dic3—42no—
69C3×C3⋊C8—24no—
70C2×C4×C8—91no—
71#382—91no—
72#382—91no—
73#340—32no—
74#340—92no—
75C22×C3×C4—22no—
76C22×C3×C4—22no—
77C22×C3×C4—21no—
78C22×C3×C4—62no—
79C22×C3×C4C22×D312yes—
80C22×Dic3—22no—
81C22×Dic3—32no—
82C22×Dic3—32no—
83C22×Dic3—62no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C2×C3×C8—34no—
87C2×C3×C8—62no—
88C2×C3×C8—62no—
89C3×C4⋊C4—22no—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—42no—
92C3×C4⋊C4—62no—
93C3×C4⋊C4—62no—
94C4⋊Dic3—22no—
95C4⋊Dic3—22no—
96C4⋊Dic3—62no—
97C4⋊Dic3—62no—
98C4⋊Dic3—122no—
99C4×Dic3—34no—
100C4×Dic3—34no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C2×C3⋊C8—22no—
104C2×C3⋊C8—22no—
105C2×C3⋊C8C4×D314yes—
106C22×C32C2×C4⋊C411yescharacteristic
107C22×C32#12411yescharacteristic
108C22×C32#12411yescharacteristic
109C22×C32#13512yes—
110C22×C32#13512yes—
111C32×C4—81no—
112C32×C4#11712yes—
113C32×C4#12512yes—
114C3⋊Dic3—24no—
115C3⋊Dic3—81no—
116C3×Dic3—82no—
117C22×C8—32no—
118C2×C4⋊C4—32no—
119C2×C4⋊C4—91no—
120C2×C4⋊C4D3211yescharacteristic
121C2×C42—91no—
122C4×C8—94no—
123#95—182no—
124#95—182no—
125C23×C3—21no—
126C23×C3D3×D412yes—
127C2×C3×C4—22no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—22no—
131C2×C3×C4—42no—
132C2×C3×C4—44no—
133C2×C3×C4—42no—
134C2×C3×C4—42no—
135C2×C3×C4—42no—
136C2×C3×C4—122no—
137C2×C3×C4—122no—
138C2×C3×C4—122no—
139C2×C3×C4C2×C4×D312yes—
140C2×C3×C4#23512yes—
141C2×C3×C4#23512yes—
142C2×C3×C4#23712yes—
143C2×C3×C4#23712yes—
144C2×C3×C4D3×Q812yes—
145C2×Dic3—34no—
146C2×Dic3—34no—
147C2×Dic3—42no—
148C2×Dic3—42no—
149C2×Dic3—42no—
150C2×Dic3—64no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—122no—
156C2×Dic3—122no—
157C2×Dic3—122no—
158C2×Dic3—124no—
159C2×Dic3—122no—
160C2×Dic3—122no—
161C2×Dic3—122no—
162C3×C8—64no—
163C3⋊C8—24no—
164C2×C32#38211yescharacteristic
165C2×C32#42712yes—
166C2×C32#48811yescharacteristic
167C2×C32#48812yes—
168C2×C32#48811yescharacteristic
169C22×C4—21no—
170C22×C4—62no—
171C22×C4—92no—
172C22×C4—181no—
173C22×C4C2×D3211yescharacteristic
174C2×C8—34no—
175C2×C8—62no—
176C2×C8—62no—
177C4⋊C4—22no—
178C4⋊C4—62no—
179C4⋊C4—62no—
180C4⋊C4—182no—
181C42—92no—
182C42—92no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—21no—
188C22×C3#88512yes—
189C22×C3#88512yes—
190C22×C3D3×C4⋊C412yes—
191C22×C3#91212yes—
192C22×C3#91612yes—
193C22×C3#91612yes—
194C22×C3#91912yes—
195C3×C4—22no—
196C3×C4—22no—
197C3×C4—82no—
198C3×C4—82no—
199C3×C4—242no—
200C3×C4#87212yes—
201C3×C4#87712yes—
202C3×C4#88912yes—
203C3×C4#88912yes—
204Dic3—64no—
205Dic3—64no—
206Dic3—82no—
207Dic3—124no—
208Dic3—242no—
209Dic3—242no—
210C32#183511yescharacteristic, complemented, Sylow
211C23#381111yescharacteristic
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—94no—
215C2×C4—122no—
216C2×C4—122no—
217C2×C4—122no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—362no—
221C2×C4—361no—
222C2×C4#379512yes—
223C2×C4#379711yescharacteristic
224C2×C4C4×D3211yescharacteristic
225C2×C4#380412yes—
226C8—64no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—21no—
232C2×C3#465012yes—
233C2×C3#476812yes—
234C2×C3#476812yes—
235C2×C3#480012yes—
236C2×C3#480012yes—
237C2×C3#486012yes—
238C2×C3#488012yes—
239C22#6388311yescharacteristic
240C22#6391311yescharacteristic
241C22#6393612yes—
242C22#6395012yes—
243C22#6395311yescharacteristic
244C4—81no—
245C4—184no—
246C4—242no—
247C4—721no—
248C4#6384712yes—
249C4#6387712yes—
250C3—21no—
251C3#6884812yescomplemented
252C2#1059053912yes—
253C2#1059057412yes—
254C2#1059124711yescharacteristic
255C2#1059140311yescharacteristic
256C2#1059153911yescharacteristic
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#1835
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
14. #63553C4semidirect
210. C32#1835semidirect
251. C3#68848semidirect

Maximal subgroups

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

subgroupindex
#105926762
#105912302
C2×#635532
C3×#45292
#105891642
#688483