Finite Group Databasebeta

← #11782812

Subgroups — #11782812

Order 1152.

279 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 279 conjugacy classes of subgroups — too many to draw. Only its 78 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×#492C211yesmaximal, characteristic
2#10588766C211yesmaximal, characteristic, complemented
3#10588758C211yesmaximal, characteristic, complemented
4#10588750C211yesmaximal, characteristic
5#10588750C211yesmaximal, characteristic
6#10588361C211yesmaximal, characteristic, complemented
7#10588131C211yesmaximal, characteristic, complemented
8#71261—31nomaximal
9C2×C9×SD16—22no—
10C9×C4⋊Q8C2211yescharacteristic
11C9×#127C2211yescharacteristic
12#63431C2211yescharacteristic
13#63431C2211yescharacteristic
14C4×C8×C9C2211yescharacteristic
15#63392—22no—
16#63392—22no—
17#63376—22no—
18#63368—22no—
19#63366—22no—
20C4×C9⋊C8C2211yescharacteristic
21C4×C9⋊C8C2211yescharacteristic
22C3×#492D311yescharacteristic
23#5093—31no—
24#5078—31no—
25#5070—31no—
26#5070—31no—
27#4681—31no—
28#4454—31no—
29C2×Q8×C9—21no—
30C2×D4×C9—21no—
31C2×D4×C9—21no—
32C2×D4×C9—21no—
33C2×Dic18—21no—
34C2×Dic18—21no—
35C9×SD16—44no—
36C2×C8×C9D412yes—
37C9×C4⋊C4—21no—
38C9×C4⋊C4—21no—
39C42×C9C2311yescharacteristic
40C4⋊Dic9—21no—
41C4⋊Dic9—21no—
42C4⋊Dic9—21no—
43C4⋊Dic9—21no—
44C2×C9⋊C8D412yes—
45C2×C9⋊C8D412yes—
46#1719—91noSylow
47C2×C3×SD16—22no—
48C3×C4⋊Q8C2×D311yescharacteristic
49C3×#127C2×D311yescharacteristic
50#869—31no—
51#869—31no—
52C3×C4×C8C2×D311yescharacteristic
53#832—62no—
54#832—62no—
55#816—62no—
56#810—62no—
57#807—62no—
58C4×C3⋊C8—31no—
59C4×C3⋊C8—31no—
60C23×C9—41no—
61Q8×C9—42no—
62D4×C9—42no—
63D4×C9—42no—
64D4×C9—42no—
65C2×C4×C9—41no—
66C2×C4×C9C2×D411yescharacteristic
67C2×C4×C9C2×D411yescharacteristic
68C2×C4×C9C2×D411yescharacteristic
69C2×Dic9—41no—
70C2×Dic9—41no—
71Dic18—42no—
72Dic18—42no—
73C8×C9—22no—
74C9⋊C8—22no—
75C9⋊C8—22no—
76#500—91no—
77#492D911yescharacteristic
78#487—91no—
79#487—91no—
80#486—91no—
81#486—91no—
82#322—91no—
83C2×C3×Q8—21no—
84C2×C3×D4—21no—
85C2×C3×D4—21no—
86C2×C3×D4—21no—
87C2×Dic6—61no—
88C2×Dic6—61no—
89C3×SD16—44no—
90C2×C3×C8#6712yes—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—21no—
93C3×C42C22×D311yescharacteristic
94C4⋊Dic3—61no—
95C4⋊Dic3—61no—
96C4⋊Dic3—61no—
97C4⋊Dic3—61no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—32no—
100C22×C9—81no—
101C22×C9—81no—
102C22×C9—81no—
103C22×C9#12711yescharacteristic
104C4×C9—81no—
105C4×C9#13512yes—
106C4×C9AGL(1,ℤ/8)12yes—
107C4×C9#13712yes—
108Dic9—81no—
109Dic9—81no—
110C2×SD16—22no—
111C4⋊Q8—91no—
112C4⋊Q8—91no—
113C4⋊Q8C2×D911yescharacteristic
114#127C2×D911yescharacteristic
115#107—182no—
116#103—182no—
117#103—182no—
118#102—182no—
119#102—182no—
120C4×C8—91no—
121C4×C8—91no—
122C4×C8C2×D911yescharacteristic
123C23×C3—41no—
124C3×Q8—42no—
125C3×D4—42no—
126C3×D4—42no—
127C3×D4—42no—
128C2×C3×C4—41no—
129C2×C3×C4D3×D411yescharacteristic
130C2×C3×C4D3×D411yescharacteristic
131C2×C3×C4C2×#6711yescharacteristic
132C2×Dic3—121no—
133C2×Dic3—121no—
134Dic6—122no—
135Dic6—122no—
136C3×C8—22no—
137C3⋊C8—62no—
138C3⋊C8—62no—
139C2×C9—161no—
140C2×C9#49511yescharacteristic
141C2×C9#49611yescharacteristic
142C2×C9#49711yescharacteristic
143C2×Q8—21no—
144C2×Q8—181no—
145C2×Q8—181no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149SD16—44no—
150C2×C8—92no—
151C2×C8—92no—
152C2×C8#61112yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—181no—
156C4⋊C4—181no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C42C22×D911yescharacteristic
160C22×C3—81no—
161C22×C3—81no—
162C22×C3—81no—
163C22×C3#94011yescharacteristic
164C3×C4—81no—
165C3×C4#91512yes—
166C3×C4#91612yes—
167C3×C4#93212yes—
168Dic3—241no—
169Dic3—241no—
170C9#171911yescharacteristic, complemented, Sylow
171C23—41no—
172Q8—42no—
173Q8—362no—
174Q8—362no—
175D4—42no—
176D4—42no—
177D4—42no—
178C2×C4—41no—
179C2×C4—361no—
180C2×C4—361no—
181C2×C4D4×D911yescharacteristic
182C2×C4D4×D911yescharacteristic
183C2×C4C2×#61111yescharacteristic
184C8—22no—
185C8—182no—
186C8—182no—
187C2×C3—161no—
188C2×C3#507411yescharacteristic
189C2×C3#516711yescharacteristic
190C2×C3#516811yescharacteristic
191C22—81no—
192C22—81no—
193C22—81no—
194C22#6350211yescharacteristic
195C4—81no—
196C4—721no—
197C4—721no—
198C4#6347712yes—
199C4#6347812yes—
200C4#6349512yes—
201C3#7126111yescharacteristic
202C2—161no—
203C2#1058875611yescharacteristic
204C2#1058884711yescharacteristic
205C2#1058884811yescharacteristic
subgroupG/H
centerC22#63502
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#492C2
socleC22×C3#940
prime radicalC3×#127C2×D3
hypercenter#492D9
hypocenterC9#1719
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #10588766C2semidirect
3. #10588758C2semidirect
6. #10588361C2semidirect
7. #10588131C2semidirect
170. C9#1719semidirect

Maximal subgroups

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

subgroupindex
C9×#4922
#105887662
#105887582
#105887502
#105883612
#105881312
#712613