Finite Group Databasebeta

← #11788909

Subgroups — #11788909

Order 1152.

924 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C32×#568C211yesmaximal, characteristic
2#10596296C211yesmaximal, characteristic
3#10592936C211yesmaximal, characteristic
4C2×#63651C212yesmaximal, complemented
5#10589425C212yesmaximal, complemented
6#72031—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C32×#131—24no—
10C2×C32×M16—22no—
11C2×C32×M16C2212yes—
12#64153—21no—
13#64145—21no—
14#64144C414yes—
15#64135C2211yescharacteristic
16#64133—22no—
17C2×#3748C2212yes—
18#63663—21no—
19#63660—21no—
20#63651—24no—
21C3×#568D314yes—
22#5825—34no—
23#5237—34no—
24C2×#824—38no—
25#4559—38no—
26C32×#41—22no—
27C32×#41—22no—
28C2×C32×Q8D411yescharacteristic
29C2×C32×D4C2×C412yes—
30C2×C32×D4D411yescharacteristic
31C22×C32×C4D412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2×C412yes—
34C2×#634—21no—
35C2×#634—21no—
36C2×#634—22no—
37C2×#634—22no—
38C32×M16—24no—
39C32×M16—22no—
40C32×M16D414yes—
41C2×C32×C8—24no—
42C2×C32×C8—22no—
43#3757—24no—
44#3757C2×C412yes—
45C4⋊(C3⋊Dic3)—21no—
46#3750—24no—
47C4×C3⋊Dic3—21no—
48#3748—22no—
49#3748—22no—
50C2×C3⋊(C3⋊C8)—22no—
51#1915—91noSylow
52C2×C3×#41C2×D314yes—
53C22×Dic6—34no—
54C3×#131—216no—
55C2×C3×M16—28no—
56C2×C3×M16C2×D318yes—
57#944—64no—
58#936—64no—
59#935—316no—
60#926—34no—
61#924—68no—
62C2×#208—38no—
63#836—64no—
64#833—64no—
65#824—616no—
66C23×C32C22⋊C412yes—
67C23×C32C22×C411yescharacteristic
68C32×Q8—22no—
69C32×D4—24no—
70C32×D4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4C22⋊C412yes—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4#4112yes—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—24no—
81#634—41no—
82#634—42no—
83#634—41no—
84C32×C8—24no—
85C3⋊(C3⋊C8)—42no—
86#568C3⋊D311yescharacteristic
87#536—91no—
88#413—91no—
89C2×#101—92no—
90#344—92no—
91C3×#41—28no—
92C3×#41—28no—
93C2×C3×Q8D1214yes—
94C2×C3×D4C4×D318yes—
95C2×C3×D4D1214yes—
96C22×C3×C4#6718yes—
97C22×C3×C4C22×D314yes—
98C22×Dic3—38no—
99C2×Dic6—64no—
100C2×Dic6—68no—
101C2×Dic6—68no—
102C2×Dic6—64no—
103C3×M16—216no—
104C3×M16—28no—
105C3×M16#67116yes—
106C2×C3×C8—216no—
107C2×C3×C8—28no—
108#217—38no—
109#217—616no—
110C4⋊Dic3—64no—
111Dic3⋊C4—616no—
112C4×Dic3—64no—
113#208—68no—
114#208—68no—
115C2×C3⋊C8—68no—
116C22×C32—22no—
117C22×C32—41no—
118C22×C32—42no—
119C22×C32C2×C22⋊C411yescharacteristic
120C22×C32C4×D412yes—
121C32×C4—22no—
122C32×C4#12011yescharacteristic
123C32×C4#12112yes—
124C32×C4#12311yescharacteristic
125C3⋊Dic3—42no—
126C3⋊Dic3—42no—
127C2×#41C2×C3⋊D311yescharacteristic
128C22×Q8—91no—
129#131—24no—
130C2×M16—22no—
131C2×M16—92no—
132C2×M16C2×C3⋊D312yes—
133C4⋊Q8—181no—
134#124—181no—
135#123—94no—
136C22⋊Q8—182no—
137#117—91no—
138#101—181no—
139#101—184no—
140#100—181no—
141C23×C3(C2×D3)⋊C418yes—
142C23×C3C2×C4×D314yes—
143C3×Q8—28no—
144C3×D4—216no—
145C3×D4—28no—
146C2×C3×C4—28no—
147C2×C3×C4—28no—
148C2×C3×C4(C2×D3)⋊C418yes—
149C2×C3×C4C2×D1214yes—
150C2×C3×C4#23518yes—
151C2×C3×C4C2×#6714yes—
152C2×C3×C4C2×#6718yes—
153C2×Dic3—68no—
154C2×Dic3—68no—
155C2×Dic3—616no—
156Dic6—124no—
157Dic6—128no—
158Dic6—124no—
159C3×C8—216no—
160C3⋊C8—128no—
161C2×C32—21no—
162C2×C32—22no—
163C2×C32—42no—
164C2×C32#38611yescharacteristic
165#41—22no—
166#41—22no—
167C2×Q8—181no—
168C2×Q8—182no—
169C2×Q8—182no—
170C2×Q8—181no—
171C2×Q8C4⋊(C3⋊D3)11yescharacteristic
172C2×D4C4×C3⋊D312yes—
173C2×D4C4⋊(C3⋊D3)11yescharacteristic
174C22×C4—92no—
175C22×C4#63812yes—
176C22×C4C22×C3⋊D311yescharacteristic
177M16—24no—
178M16—22no—
179M16—182no—
180M16—182no—
181M16#63814yes—
182C2×C8—24no—
183C2×C8—22no—
184C2×C8—182no—
185C4⋊C4—184no—
186C4⋊C4—181no—
187C22⋊C4—92no—
188C22⋊C4—184no—
189C42—181no—
190C22×C3—28no—
191C22×C3—44no—
192C22×C3—48no—
193C22×C3C2×(C2×D3)⋊C414yes—
194C22×C3C4×#6718yes—
195C3×C4—28no—
196C3×C4#92914yes—
197C3×C4#93018yes—
198C3×C4#95314yes—
199Dic3—128no—
200Dic3—128no—
201C32#191511yescharacteristic, complemented, Sylow
202C23#375212yes—
203C23C2×C4×C3⋊D311yescharacteristic
204Q8—22no—
205Q8—361no—
206Q8—362no—
207Q8—361no—
208D4—24no—
209D4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—184no—
215C2×C4#375212yes—
216C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
217C2×C4#382812yes—
218C2×C4C2×#63811yescharacteristic
219C2×C4C2×#63812yes—
220C8—24no—
221C8—362no—
222C2×C3—24no—
223C2×C3—28no—
224C2×C3—48no—
225C2×C3#521314yes—
226C22—22no—
227C22—41no—
228C22—42no—
229C22C2×#375211yescharacteristic
230C22C4×#63812yes—
231C4—22no—
232C4—362no—
233C4—362no—
234C4#6413811yescharacteristic
235C4#6413912yes—
236C4#6416211yescharacteristic
237C3#7203114yescomplemented
238C2—21no—
239C2—22no—
240C2—42no—
241C2#1059291211yescharacteristic
subgroupG/H
centerC2#10592912
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#568C2
socleC2×C32#386
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenter#568C3⋊D3
hypocenterC32#1915
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
4. C2×#63651C2semidirect
5. #10589425C2semidirect
201. C32#1915semidirect
237. C3#72031semidirect

Maximal subgroups

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

subgroupindex
C32×#5682
#105962962
#105929362
C2×#636512
#105894252
#720313