Finite Group Databasebeta

← #11788908

Subgroups — #11788908

Order 1152.

462 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C9×#568C211yesmaximal, characteristic
2#10589927C211yesmaximal, characteristic
3#10588915C211yesmaximal, characteristic
4C2×#63382C212yesmaximal, complemented
5#10588232C212yesmaximal, complemented
6#72031—31nomaximal
7C2×C9×#41C2211yescharacteristic
8C22×Dic18C2211yescharacteristic
9C9×#131—24no—
10C2×C9×M16—22no—
11C2×C9×M16C2212yes—
12#63506—21no—
13#63498—21no—
14#63497C414yes—
15#63488C2211yescharacteristic
16#63486—22no—
17C2×#3667C2212yes—
18#63394—21no—
19#63391—21no—
20#63382—24no—
21C3×#568D311yescharacteristic
22#5825—31no—
23#5237—31no—
24C2×#824—32no—
25#4559—32no—
26C9×#41—22no—
27C9×#41—22no—
28C2×Q8×C9D411yescharacteristic
29C2×D4×C9C2×C412yes—
30C2×D4×C9D411yescharacteristic
31C22×C4×C9D412yes—
32C22×C4×C9C2311yescharacteristic
33C22×Dic9C2×C412yes—
34C2×Dic18—21no—
35C2×Dic18—22no—
36C2×Dic18—21no—
37C2×Dic18—22no—
38C9×M16—24no—
39C9×M16—22no—
40C9×M16D414yes—
41C2×C8×C9—24no—
42C2×C8×C9—22no—
43#3676—24no—
44#3676C2×C412yes—
45C4⋊Dic9—21no—
46Dic9⋊C4—24no—
47C4×Dic9—21no—
48#3667—22no—
49#3667—22no—
50C2×C9⋊C8—22no—
51#1915—91noSylow
52C2×C3×#41C2×D311yescharacteristic
53C22×Dic6—31no—
54C3×#131—24no—
55C2×C3×M16—22no—
56C2×C3×M16C2×D312yes—
57#944—61no—
58#936—61no—
59#935—34no—
60#926—31no—
61#924—62no—
62C2×#208—32no—
63#836—61no—
64#833—61no—
65#824—64no—
66C23×C9C22⋊C412yes—
67C23×C9C22×C411yescharacteristic
68Q8×C9—22no—
69D4×C9—24no—
70D4×C9—22no—
71C2×C4×C9—22no—
72C2×C4×C9—22no—
73C2×C4×C9C22⋊C412yes—
74C2×C4×C9C2×D411yescharacteristic
75C2×C4×C9C2×D412yes—
76C2×C4×C9C2×D411yescharacteristic
77C2×C4×C9#4112yes—
78C2×Dic9—22no—
79C2×Dic9—22no—
80C2×Dic9—24no—
81Dic18—41no—
82Dic18—42no—
83Dic18—41no—
84C8×C9—24no—
85C9⋊C8—42no—
86#568D911yescharacteristic
87#536—91no—
88#413—91no—
89C2×#101—92no—
90#344—92no—
91C3×#41—22no—
92C3×#41—22no—
93C2×C3×Q8D1211yescharacteristic
94C2×C3×D4C4×D312yes—
95C2×C3×D4D1211yescharacteristic
96C22×C3×C4#6712yes—
97C22×C3×C4C22×D311yescharacteristic
98C22×Dic3—32no—
99C2×Dic6—61no—
100C2×Dic6—62no—
101C2×Dic6—62no—
102C2×Dic6—61no—
103C3×M16—24no—
104C3×M16—22no—
105C3×M16#6714yes—
106C2×C3×C8—24no—
107C2×C3×C8—22no—
108#217—32no—
109#217—64no—
110C4⋊Dic3—61no—
111Dic3⋊C4—64no—
112C4×Dic3—61no—
113#208—62no—
114#208—62no—
115C2×C3⋊C8—62no—
116C22×C9—22no—
117C22×C9—41no—
118C22×C9—42no—
119C22×C9C2×C22⋊C411yescharacteristic
120C22×C9C4×D412yes—
121C4×C9—22no—
122C4×C9#12011yescharacteristic
123C4×C9#12112yes—
124C4×C9#12311yescharacteristic
125Dic9—42no—
126Dic9—42no—
127C2×#41C2×D911yescharacteristic
128C22×Q8—91no—
129#131—24no—
130C2×M16—22no—
131C2×M16—92no—
132C2×M16C2×D912yes—
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)⋊C412yes—
142C23×C3C2×C4×D311yescharacteristic
143C3×Q8—22no—
144C3×D4—24no—
145C3×D4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4(C2×D3)⋊C412yes—
149C2×C3×C4C2×D1211yescharacteristic
150C2×C3×C4#23512yes—
151C2×C3×C4C2×#6711yescharacteristic
152C2×C3×C4C2×#6712yes—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—64no—
156Dic6—121no—
157Dic6—122no—
158Dic6—121no—
159C3×C8—24no—
160C3⋊C8—122no—
161C2×C9—21no—
162C2×C9—22no—
163C2×C9—42no—
164C2×C9#38611yescharacteristic
165#41—22no—
166#41—22no—
167C2×Q8—181no—
168C2×Q8—182no—
169C2×Q8—182no—
170C2×Q8—181no—
171C2×Q8D3611yescharacteristic
172C2×D4C4×D912yes—
173C2×D4D3611yescharacteristic
174C22×C4—92no—
175C22×C4#61112yes—
176C22×C4C22×D911yescharacteristic
177M16—24no—
178M16—22no—
179M16—182no—
180M16—182no—
181M16#61114yes—
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—22no—
191C22×C3—41no—
192C22×C3—42no—
193C22×C3C2×(C2×D3)⋊C411yescharacteristic
194C22×C3C4×#6712yes—
195C3×C4—22no—
196C3×C4#92911yescharacteristic
197C3×C4#93012yes—
198C3×C4#95311yescharacteristic
199Dic3—122no—
200Dic3—122no—
201C9#191511yescharacteristic, complemented, Sylow
202C23(C2×D9)⋊C412yes—
203C23C2×C4×D911yescharacteristic
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(C2×D9)⋊C412yes—
216C2×C4C2×D3611yescharacteristic
217C2×C4#369712yes—
218C2×C4C2×#61111yescharacteristic
219C2×C4C2×#61112yes—
220C8—24no—
221C8—362no—
222C2×C3—21no—
223C2×C3—22no—
224C2×C3—42no—
225C2×C3#521311yescharacteristic
226C22—22no—
227C22—41no—
228C22—42no—
229C22C2×(C2×D9)⋊C411yescharacteristic
230C22C4×#61112yes—
231C4—22no—
232C4—362no—
233C4—362no—
234C4#6349111yescharacteristic
235C4#6349212yes—
236C4#6351511yescharacteristic
237C3#7203111yescharacteristic
238C2—21no—
239C2—22no—
240C2—42no—
241C2#1058889311yescharacteristic
subgroupG/H
centerC2#10588893
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#568C2
socleC2×C3#5213
prime radicalC2×C3×#41C2×D3
cosocleC22×C4×C9C23
hypercenter#568D9
hypocenterC9#1915
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
4. C2×#63382C2semidirect
5. #10588232C2semidirect
201. C9#1915semidirect

Maximal subgroups

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

subgroupindex
C9×#5682
#105899272
#105889152
C2×#633822
#105882322
#720313