Finite Group Databasebeta

← #11778585

Subgroups — #11778585

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
2#10588661C211yesmaximal, characteristic
3#10588401C212yesmaximal
4C9×#324C211yesmaximal, characteristic
5#10588144C212yesmaximal
6#68140—31nomaximal
7C2×C9×C4⋊C4C2211yescharacteristic
8#63488—21no—
9C2×C4⋊Dic9C2211yescharacteristic
10#63486—21no—
11#63486C2212yes—
12C2×Dic9⋊C4—21no—
13#63452—22no—
14#63450—22no—
15C9×C22⋊C8C2212yes—
16C9⋊#95—21no—
17C9⋊#95C2211yescharacteristic
18#63377—22no—
19#63376—22no—
20#5500—31no—
21#4981—31no—
22#4721—32no—
23C3×#324D311yescharacteristic
24#4467—32no—
25C22×C4×C9D411yescharacteristic
26C22×C4×C9D411yescharacteristic
27C22×C4×C9C2311yescharacteristic
28C22×Dic9—21no—
29C22×Dic9—21no—
30C2×Dic18—21no—
31C2×Dic18D412yes—
32C2×C8×C9—22no—
33C9×C4⋊C4—22no—
34#3676—22no—
35C4⋊Dic9—21no—
36C4⋊Dic9—21no—
37C4⋊Dic9—21no—
38C4⋊Dic9—22no—
39C4⋊Dic9D412yes—
40Dic9⋊C4—22no—
41Dic9⋊C4—22no—
42Dic9⋊C4—42no—
43C4×Dic9—22no—
44#1611—91noSylow
45C2×C3×C4⋊C4C2×D311yescharacteristic
46#926—61no—
47C2×C4⋊Dic3—31no—
48#924—32no—
49#924—61no—
50C2×Dic3⋊C4—61no—
51#890—62no—
52#888—62no—
53C3×C22⋊C8C2×D312yes—
54C3⋊#95—31no—
55C3⋊#95—61no—
56#817—62no—
57#816—62no—
58C23×C9C2×D411yescharacteristic
59C2×C4×C9—21no—
60C2×C4×C9—21no—
61C2×C4×C9—21no—
62C2×C4×C9—41no—
63C2×C4×C9—41no—
64C2×C4×C9SD1612yes—
65C2×C4×C9C2×D412yes—
66C2×Dic9—22no—
67C2×Dic9—22no—
68C2×Dic9—22no—
69C2×Dic9—41no—
70C2×Dic9—41no—
71C2×Dic9—41no—
72C2×Dic9—41no—
73C2×Dic9—41no—
74Dic18—42no—
75Dic18—81no—
76C8×C9—42no—
77#544—91no—
78#483—92no—
79#398—91no—
80#328—92no—
81#324D911yescharacteristic
82C22×C3×C4D1211yescharacteristic
83C22×C3×C4D1211yescharacteristic
84C22×C3×C4C22×D311yescharacteristic
85C22×Dic3—61no—
86C22×Dic3—61no—
87C2×Dic6—32no—
88C2×Dic6—61no—
89C2×C3×C8—22no—
90C3×C4⋊C4—22no—
91#217—62no—
92C4⋊Dic3—32no—
93C4⋊Dic3—61no—
94C4⋊Dic3—61no—
95C4⋊Dic3—61no—
96C4⋊Dic3—62no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99Dic3⋊C4—122no—
100C4×Dic3—62no—
101C22×C9—21no—
102C22×C9—21no—
103C22×C9#12011yescharacteristic
104C22×C9C2×SD1611yescharacteristic
105C22×C9#13711yescharacteristic
106C4×C9—22no—
107C4×C9—22no—
108C4×C9—41no—
109Dic9—42no—
110Dic9—42no—
111Dic9—42no—
112Dic9—81no—
113C4⋊Q8—182no—
114#125—182no—
115C22⋊Q8—92no—
116C22⋊Q8—181no—
117#117—181no—
118C2×C4⋊C4—91no—
119C2×C4⋊C4—181no—
120C2×C4⋊C4C2×D911yescharacteristic
121#106—182no—
122#103—182no—
123C22⋊C8C2×D912yes—
124#95—91no—
125#95—181no—
126C23×C3C2×D1211yescharacteristic
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—41no—
131C2×C3×C4—41no—
132C2×C3×C4#20412yes—
133C2×C3×C4D3×D412yes—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—121no—
138C2×Dic3—121no—
139C2×Dic3—121no—
140C2×Dic3—121no—
141C2×Dic3—121no—
142Dic6—122no—
143Dic6—241no—
144C3×C8—42no—
145C2×C9—21no—
146C2×C9—21no—
147C2×C9#44811yescharacteristic
148C2×C9#45611yescharacteristic
149C2×C9#45811yescharacteristic
150C2×Q8—92no—
151C2×Q8—181no—
152C22×C4—181no—
153C22×C4—181no—
154C22×C4D3611yescharacteristic
155C22×C4D3611yescharacteristic
156C22×C4C22×D911yescharacteristic
157C2×C8—22no—
158C4⋊C4—22no—
159C4⋊C4—92no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C4⋊C4—181no—
163C4⋊C4—182no—
164C4⋊C4—182no—
165C4⋊C4—182no—
166C4⋊C4—362no—
167C22⋊C4—182no—
168C42—182no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3#88211yescharacteristic
172C22×C3C2×#20411yescharacteristic
173C22×C3#90911yescharacteristic
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—41no—
177Dic3—122no—
178Dic3—122no—
179Dic3—122no—
180Dic3—241no—
181C9#161111yescharacteristic, complemented, Sylow
182C23C2×D3611yescharacteristic
183Q8—362no—
184Q8—721no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—182no—
191C2×C4—182no—
192C2×C4—182no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4#366412yes—
199C2×C4D4×D912yes—
200C8—42no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3#473811yescharacteristic
204C2×C3#474211yescharacteristic
205C2×C3#475211yescharacteristic
206C22—21no—
207C22—21no—
208C22#6344411yescharacteristic
209C22C2×#366411yescharacteristic
210C22#6347111yescharacteristic
211C4—22no—
212C4—22no—
213C4—41no—
214C4—362no—
215C4—362no—
216C4—362no—
217C4—721no—
218C3#6814011yescharacteristic
219C2—21no—
220C2—21no—
221C2#1058840411yescharacteristic
222C2#1058842211yescharacteristic
223C2#1058843211yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3#882
prime radicalC23×C3C2×D12
hypercenter#324D9
hypocenterC9#1611
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

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
#105886612
#105884012
C9×#3242
#105881442
#681403