Finite Group Databasebeta

← #11778576

Subgroups — #11778576

Order 1152.

315 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 72 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#10589602C211yesmaximal, characteristic
2C9×#398C211yesmaximal, characteristic
3#10588647C212yesmaximal
4#10588205C211yesmaximal, characteristic
5#10588128C212yesmaximal
6#69713—31nomaximal
7C2×C9×C4⋊C4—21no—
8C2×C9×C4⋊C4C2211yescharacteristic
9C2×C9×C4⋊C4C2211yescharacteristic
10#63488—21no—
11#63486—21no—
12#63486C2212yes—
13#63452—22no—
14#63450—22no—
15C9×#95—21no—
16C9×#95C2211yescharacteristic
17#63389C2212yes—
18#63368—22no—
19#63367—22no—
20#5500—31no—
21C3×#398D311yescharacteristic
22#4971—32no—
23#4528—31no—
24#4452—32no—
25C22×C4×C9—21no—
26C22×C4×C9—21no—
27C22×C4×C9D411yescharacteristic
28C22×C4×C9D411yescharacteristic
29C22×C4×C9C2311yescharacteristic
30C2×Dic18—21no—
31C2×Dic18D412yes—
32C9×C4⋊C4—22no—
33C9×C4⋊C4—22no—
34C9×C4⋊C4—42no—
35#3676—22no—
36C4⋊Dic9—21no—
37C4⋊Dic9—21no—
38C4⋊Dic9—21no—
39C4⋊Dic9D412yes—
40Dic9⋊C4—22no—
41Dic9⋊C4—22no—
42C4×Dic9—22no—
43C2×C9⋊C8—22no—
44#1611—91noSylow
45C2×C3×C4⋊C4—21no—
46C2×C3×C4⋊C4C2×D311yescharacteristic
47C2×C3×C4⋊C4C2×D311yescharacteristic
48#926—61no—
49#924—32no—
50#924—61no—
51#890—62no—
52#888—62no—
53C3×#95—21no—
54C3×#95C2×D311yescharacteristic
55#830—32no—
56#810—62no—
57#808—62no—
58C23×C9C2×D411yescharacteristic
59C2×C4×C9—21no—
60C2×C4×C9—21no—
61C2×C4×C9—22no—
62C2×C4×C9—21no—
63C2×C4×C9—41no—
64C2×C4×C9—41no—
65C2×C4×C9—41no—
66C2×C4×C9—41no—
67C2×C4×C9—41no—
68C2×C4×C9—41no—
69C2×C4×C9—41no—
70C2×C4×C9SD1612yes—
71C2×C4×C9C2×D412yes—
72C2×Dic9—22no—
73C2×Dic9—22no—
74Dic18—42no—
75Dic18—81no—
76C9⋊C8—42no—
77#544—91no—
78#483—92no—
79#398D911yescharacteristic
80#328—92no—
81#324—91no—
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4#6711yescharacteristic
85C22×C3×C4#6711yescharacteristic
86C22×C3×C4C22×D311yescharacteristic
87C2×Dic6—32no—
88C2×Dic6—61no—
89C3×C4⋊C4—22no—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—42no—
92#217—62no—
93C4⋊Dic3—32no—
94C4⋊Dic3—61no—
95C4⋊Dic3—61no—
96C4⋊Dic3—61no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99C4×Dic3—62no—
100C2×C3⋊C8—62no—
101C22×C9—21no—
102C22×C9—21no—
103C22×C9#12011yescharacteristic
104C22×C9C2×SD1611yescharacteristic
105C22×C9#13711yescharacteristic
106C4×C9—22no—
107C4×C9—22no—
108C4×C9—42no—
109C4×C9—41no—
110C4×C9—81no—
111Dic9—42no—
112Dic9—42no—
113C4⋊Q8—182no—
114#125—182no—
115C22⋊Q8—92no—
116C22⋊Q8—181no—
117#117—181no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4C2×D911yescharacteristic
120C2×C4⋊C4C2×D911yescharacteristic
121#106—182no—
122#103—182no—
123C22⋊C8—92no—
124#95—21no—
125#95C2×D911yescharacteristic
126C23×C3C2×#6711yescharacteristic
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4#21412yes—
139C2×C3×C4D3×D412yes—
140C2×Dic3—62no—
141C2×Dic3—62no—
142Dic6—122no—
143Dic6—241no—
144C3⋊C8—122no—
145C2×C9—21no—
146C2×C9—21no—
147C2×C9#44811yescharacteristic
148C2×C9#45611yescharacteristic
149C2×C9#45811yescharacteristic
150C2×Q8—92no—
151C2×Q8—181no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4#61111yescharacteristic
155C22×C4#61111yescharacteristic
156C22×C4C22×D911yescharacteristic
157C2×C8—182no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—42no—
161C4⋊C4—92no—
162C4⋊C4—181no—
163C4⋊C4—181no—
164C4⋊C4—181no—
165C4⋊C4—182no—
166C4⋊C4—182no—
167C22⋊C4—182no—
168C42—182no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3C2×#21411yescharacteristic
172C22×C3#93711yescharacteristic
173C22×C3#95111yescharacteristic
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—42no—
177C3×C4—41no—
178C3×C4—81no—
179Dic3—122no—
180Dic3—122no—
181C9#161111yescharacteristic, complemented, Sylow
182C23C2×#61111yescharacteristic
183Q8—362no—
184Q8—721no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4#367212yes—
199C2×C4D4×D912yes—
200C8—362no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3#504011yescharacteristic
204C2×C3#505311yescharacteristic
205C2×C3#509511yescharacteristic
206C22—21no—
207C22—21no—
208C22C2×#367211yescharacteristic
209C22#6349911yescharacteristic
210C22#6351111yescharacteristic
211C4—22no—
212C4—22no—
213C4—42no—
214C4—41no—
215C4—81no—
216C4—362no—
217C4—362no—
218C3#6971311yescharacteristic
219C2—21no—
220C2—21no—
221C2#1058871611yescharacteristic
222C2#1058873311yescharacteristic
223C2#1058877511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#398C2
socleC22×C3#937
prime radicalC23×C3C2×#67
hypercenter#398D9
hypocenterC9#1611
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
181. C9#1611semidirect

Maximal subgroups

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

subgroupindex
#105896022
C9×#3982
#105886472
#105882052
#105881282
#697133