Finite Group Databasebeta

← #11778806

Subgroups — #11778806

Order 1152.

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

normal subgroups only

This group has 303 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#10588724C212yesmaximal
3#10588666C211yesmaximal, characteristic
4#10588215C212yesmaximal
5#10588205C211yesmaximal, characteristic
6#71899—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
14#63395—22no—
15C9⋊#95—21no—
16C9⋊#95—21no—
17C9⋊#95C2211yescharacteristic
18#63389C2212yes—
19#63366—22no—
20C3×#544D311yescharacteristic
21#5044—32no—
22#4986—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—
42C2×C9⋊C8—22no—
43#1617—91noSylow
44C3×C4⋊Q8—22no—
45C3×#125—22no—
46C3×C22⋊Q8—21no—
47C3×C22⋊Q8C2×D312yes—
48C3×#117—21no—
49C2×C3×C4⋊C4C2×D311yescharacteristic
50C2×C4⋊Dic3—31no—
51#835—62no—
52C3⋊#95—31no—
53C3⋊#95—61no—
54C3⋊#95—61no—
55#830—32no—
56#807—62no—
57C23×C9C2×D411yescharacteristic
58Q8×C9—42no—
59Q8×C9—81no—
60C2×C4×C9—21no—
61C2×C4×C9—21no—
62C2×C4×C9—22no—
63C2×C4×C9—22no—
64C2×C4×C9—21no—
65C2×C4×C9—41no—
66C2×C4×C9—41no—
67C2×C4×C9Q1612yes—
68C2×C4×C9C2×D412yes—
69C2×Dic9—41no—
70C2×Dic9—41no—
71C2×Dic9—42no—
72C2×Dic9—41no—
73C2×Dic9—41no—
74C9⋊C8—42no—
75#544D911yescharacteristic
76#484—92no—
77#400—91no—
78#328—92no—
79#324—91no—
80C2×C3×Q8—21no—
81C2×C3×Q8#6712yes—
82C22×C3×C4#6711yescharacteristic
83C22×C3×C4#6711yescharacteristic
84C22×C3×C4C22×D311yescharacteristic
85C22×Dic3—61no—
86C22×Dic3—61no—
87C3×C4⋊C4—21no—
88C3×C4⋊C4—21no—
89C3×C4⋊C4—21no—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—22no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4#6712yes—
94C3×C22⋊C4—22no—
95C3×C42—22no—
96C4⋊Dic3—62no—
97C2×C3⋊C8—62no—
98C22×C9—21no—
99C22×C9—21no—
100C22×C9#12011yescharacteristic
101C22×C9C2×Q1611yescharacteristic
102C22×C9#13711yescharacteristic
103C4×C9—22no—
104C4×C9—22no—
105C4×C9—42no—
106C4×C9—41no—
107C4×C9—42no—
108Dic9—81no—
109Dic9—81no—
110C4⋊Q8—22no—
111#125—22no—
112C22⋊Q8—21no—
113C22⋊Q8C2×D912yes—
114#117—21no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4C2×D911yescharacteristic
117#107—182no—
118#103—182no—
119C22⋊C8—92no—
120#95—91no—
121#95—181no—
122#95—181no—
123C23×C3C2×#6711yescharacteristic
124C3×Q8—42no—
125C3×Q8—81no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4#21612yes—
134C2×C3×C4C2×#6712yes—
135C2×Dic3—121no—
136C2×Dic3—121no—
137C2×Dic3—122no—
138C2×Dic3—121no—
139C2×Dic3—121no—
140C3⋊C8—122no—
141C2×C9—21no—
142C2×C9—21no—
143C2×C9#45111yescharacteristic
144C2×C9#45411yescharacteristic
145C2×C9#45811yescharacteristic
146C2×Q8—21no—
147C2×Q8#61112yes—
148C22×C4—181no—
149C22×C4—181no—
150C22×C4#61111yescharacteristic
151C22×C4#61111yescharacteristic
152C22×C4C22×D911yescharacteristic
153C2×C8—182no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—182no—
161C4⋊C4#61112yes—
162C22⋊C4—22no—
163C42—22no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3#94211yescharacteristic
167C22×C3C2×#21611yescharacteristic
168C22×C3#95311yescharacteristic
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—41no—
172C3×C4—42no—
173C3×C4—42no—
174Dic3—241no—
175Dic3—241no—
176C9#161711yescharacteristic, complemented, Sylow
177C23C2×#61111yescharacteristic
178Q8—42no—
179Q8—81no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—361no—
188C2×C4—361no—
189C2×C4—362no—
190C2×C4—361no—
191C2×C4—361no—
192C2×C4#367412yes—
193C2×C4C2×#61112yes—
194C8—362no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3#522811yescharacteristic
198C2×C3#524311yescharacteristic
199C2×C3#524511yescharacteristic
200C22—21no—
201C22—21no—
202C22C2×#367411yescharacteristic
203C22#6350511yescharacteristic
204C22#6351511yescharacteristic
205C4—22no—
206C4—22no—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—721no—
211C4—721no—
212C3#7189911yescharacteristic
213C2—21no—
214C2—21no—
215C2#1058890711yescharacteristic
216C2#1058892311yescharacteristic
217C2#1058892611yescharacteristic
subgroupG/H
centerC22#63515
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#544C2
socleC22×C3#953
prime radicalC23×C3C2×#67
hypercenter#544D9
hypocenterC9#1617
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
176. C9#1617semidirect

Maximal subgroups

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

subgroupindex
C9×#5442
#105887242
#105886662
#105882152
#105882052
#718993