Finite Group Databasebeta

← #11778579

Subgroups — #11778579

Order 1152.

315 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 80 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×#544C211yesmaximal, characteristic
2#10588723C212yesmaximal
3#10588661C211yesmaximal, characteristic
4#10588215C212yesmaximal
5#10588205C211yesmaximal, characteristic
6#71898—31nomaximal
7C9×C4⋊Q8—22no—
8C9×#125—22no—
9C9×C22⋊Q8—21no—
10C9×C22⋊Q8C2212yes—
11C9×#117—21no—
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic9C2211yescharacteristic
14C2×Dic9⋊C4—21no—
15#63395—22no—
16C9⋊#95—21no—
17C9⋊#95C2211yescharacteristic
18#63389C2212yes—
19#63367—22no—
20C3×#544D311yescharacteristic
21#5043—32no—
22#4981—31no—
23#4538—32no—
24#4528—31no—
25C2×Q8×C9—21no—
26C2×Q8×C9D412yes—
27C22×C4×C9D411yescharacteristic
28C22×C4×C9D411yescharacteristic
29C22×C4×C9C2311yescharacteristic
30C22×Dic9—21no—
31C22×Dic9—21no—
32C9×C4⋊C4—21no—
33C9×C4⋊C4—21no—
34C9×C4⋊C4—21no—
35C9×C4⋊C4—22no—
36C9×C4⋊C4—22no—
37C9×C4⋊C4—22no—
38C9×C4⋊C4D412yes—
39C9×C22⋊C4—22no—
40C42×C9—22no—
41C4⋊Dic9—22no—
42Dic9⋊C4—42no—
43C2×C9⋊C8—22no—
44#1611—91noSylow
45C3×C4⋊Q8—22no—
46C3×#125—22no—
47C3×C22⋊Q8—21no—
48C3×C22⋊Q8C2×D312yes—
49C3×#117—21no—
50C2×C3×C4⋊C4C2×D311yescharacteristic
51C2×C4⋊Dic3—31no—
52C2×Dic3⋊C4—61no—
53#835—62no—
54C3⋊#95—31no—
55C3⋊#95—61no—
56#830—32no—
57#808—62no—
58C23×C9C2×D411yescharacteristic
59Q8×C9—42no—
60Q8×C9—81no—
61C2×C4×C9—21no—
62C2×C4×C9—21no—
63C2×C4×C9—22no—
64C2×C4×C9—22no—
65C2×C4×C9—21no—
66C2×C4×C9—41no—
67C2×C4×C9—41no—
68C2×C4×C9SD1612yes—
69C2×C4×C9C2×D412yes—
70C2×Dic9—22no—
71C2×Dic9—41no—
72C2×Dic9—41no—
73C2×Dic9—41no—
74C2×Dic9—41no—
75C2×Dic9—41no—
76C9⋊C8—42no—
77#544D911yescharacteristic
78#483—92no—
79#398—91no—
80#328—92no—
81#324—91no—
82C2×C3×Q8—21no—
83C2×C3×Q8#6712yes—
84C22×C3×C4#6711yescharacteristic
85C22×C3×C4#6711yescharacteristic
86C22×C3×C4C22×D311yescharacteristic
87C22×Dic3—61no—
88C22×Dic3—61no—
89C3×C4⋊C4—21no—
90C3×C4⋊C4—21no—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4#6712yes—
96C3×C22⋊C4—22no—
97C3×C42—22no—
98C4⋊Dic3—62no—
99Dic3⋊C4—122no—
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—42no—
111Dic9—42no—
112Dic9—81no—
113C4⋊Q8—22no—
114#125—22no—
115C22⋊Q8—21no—
116C22⋊Q8C2×D912yes—
117#117—21no—
118C2×C4⋊C4—91no—
119C2×C4⋊C4—181no—
120C2×C4⋊C4C2×D911yescharacteristic
121#106—182no—
122#103—182no—
123C22⋊C8—92no—
124#95—91no—
125#95—181no—
126C23×C3C2×#6711yescharacteristic
127C3×Q8—42no—
128C3×Q8—81no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—41no—
135C2×C3×C4—41no—
136C2×C3×C4#21512yes—
137C2×C3×C4C2×#6712yes—
138C2×Dic3—62no—
139C2×Dic3—121no—
140C2×Dic3—121no—
141C2×Dic3—121no—
142C2×Dic3—121no—
143C2×Dic3—121no—
144C3⋊C8—122no—
145C2×C9—21no—
146C2×C9—21no—
147C2×C9#44811yescharacteristic
148C2×C9#45611yescharacteristic
149C2×C9#45811yescharacteristic
150C2×Q8—21no—
151C2×Q8#61112yes—
152C22×C4—181no—
153C22×C4—181no—
154C22×C4#61111yescharacteristic
155C22×C4#61111yescharacteristic
156C22×C4C22×D911yescharacteristic
157C2×C8—182no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—182no—
165C4⋊C4—362no—
166C4⋊C4#61112yes—
167C22⋊C4—22no—
168C42—22no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3C2×#21511yescharacteristic
172C22×C3#94211yescharacteristic
173C22×C3#95311yescharacteristic
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—41no—
177C3×C4—42no—
178C3×C4—42no—
179Dic3—122no—
180Dic3—241no—
181C9#161111yescharacteristic, complemented, Sylow
182C23C2×#61111yescharacteristic
183Q8—42no—
184Q8—81no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—182no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4#367512yes—
199C2×C4C2×#61112yes—
200C8—362no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3#522711yescharacteristic
204C2×C3#524311yescharacteristic
205C2×C3#524611yescharacteristic
206C22—21no—
207C22—21no—
208C22C2×#367511yescharacteristic
209C22#6350511yescharacteristic
210C22#6351511yescharacteristic
211C4—22no—
212C4—22no—
213C4—41no—
214C4—42no—
215C4—42no—
216C4—362no—
217C4—721no—
218C3#7189811yescharacteristic
219C2—21no—
220C2—21no—
221C2#1058890811yescharacteristic
222C2#1058892311yescharacteristic
223C2#1058892511yescharacteristic
subgroupG/H
centerC22#63515
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#544C2
socleC22×C3#953
prime radicalC23×C3C2×#67
hypercenter#544D9
hypocenterC9#1611
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

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
C9×#5442
#105887232
#105886612
#105882152
#105882052
#718983