Finite Group Databasebeta

← #11776049

Subgroups — #11776049

Order 1152.

291 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 291 conjugacy classes of subgroups — too many to draw. Only its 74 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#10589790C211yesmaximal, characteristic
2#10588386C212yesmaximal
3C9×#330C211yesmaximal, characteristic, complemented
4#10588220C211yesmaximal, characteristic, complemented
5#10588141C212yesmaximal, complemented
6#68369—31nomaximal
7C9×#125C2211yescharacteristic
8#63458—22no—
9#63454C412yes—
10#63450C412yes—
11#63449—22no—
12C42×D9C2211yescharacteristic
13#63432C2211yescharacteristic
14C9×#97C2212yes—
15(C2×D9)⋊C8—22no—
16Dic9⋊C8—22no—
17#63362C2212yes—
18#5688—31no—
19#4705—32no—
20C3×#330D311yescharacteristic
21#4543—31no—
22#4465—32no—
23C2×C4×D9C2×C411yescharacteristic
24C2×C4×D9D412yes—
25C2×Dic18—22no—
26C2×C8×C9—22no—
27C9×C4⋊C4—22no—
28C9×C4⋊C4C2×C412yes—
29C42×C9C2311yescharacteristic
30(C2×D9)⋊C4—22no—
31C4⋊Dic9C2×C412yes—
32Dic9⋊C4—22no—
33Dic9⋊C4—22no—
34C4×Dic9—22no—
35C4×Dic9C2×C411yescharacteristic
36C4×Dic9D412yes—
37C2×C9⋊C8—22no—
38#1537—91noSylow
39C3×#125C2×D311yescharacteristic
40#896—62no—
41#892—32no—
42#888—32no—
43#887—62no—
44C42×D3—31no—
45#870—31no—
46C3×#97C2×D312yes—
47(C2×D3)⋊C8—62no—
48Dic3⋊C8—62no—
49#803—32no—
50C22×D9C22⋊C411yescharacteristic
51C2×C4×C9—22no—
52C2×C4×C9C22×C411yescharacteristic
53C2×C4×C9C2×D412yes—
54C2×Dic9—22no—
55C2×Dic9C22⋊C412yes—
56C2×Dic9C22⋊C411yescharacteristic
57C4×D9—22no—
58C4×D9—42no—
59Dic18—44no—
60C8×C9—42no—
61C9⋊C8—42no—
62#533—91no—
63#432—92no—
64#330—91no—
65#330—92no—
66#330D911yescharacteristic, complemented
67C2×C4×D3—31no—
68C2×C4×D3—32no—
69C2×Dic6—62no—
70C2×C3×C8—22no—
71C3×C4⋊C4—22no—
72C3×C4⋊C4C4×D312yes—
73C3×C42C22×D311yescharacteristic
74(C2×D3)⋊C4—62no—
75C4⋊Dic3—32no—
76Dic3⋊C4—62no—
77Dic3⋊C4—62no—
78C4×Dic3—31no—
79C4×Dic3—32no—
80C4×Dic3—62no—
81C2×C3⋊C8—62no—
82C22×C9C2×C22⋊C411yescharacteristic
83C2×D9—21no—
84C2×D9—22no—
85C4×C9—21no—
86C4×C9—22no—
87C4×C9—42no—
88Dic9—22no—
89Dic9—42no—
90Dic9#10112yes—
91C4⋊Q8—92no—
92#125—91no—
93#125C2×D911yescharacteristic
94C22⋊Q8—182no—
95C4×Q8—182no—
96#117—92no—
97C2×C42—91no—
98C4⋊C8—182no—
99C22⋊C8—182no—
100#97—92no—
101#97C2×D912yes—
102C22×D3—31no—
103C2×C3×C4—22no—
104C2×C3×C4C2×C4×D311yescharacteristic
105C2×C3×C4D3×D412yes—
106C2×Dic3—31no—
107C2×Dic3—32no—
108C2×Dic3—62no—
109C4×D3—62no—
110C4×D3—122no—
111Dic6—124no—
112C3×C8—42no—
113C3⋊C8—122no—
114C2×C9C2×#10111yescharacteristic
115C2×C9#42112yes—
116D9—41no—
117C2×Q8—182no—
118C22×C4—91no—
119C22×C4—92no—
120C2×C8—22no—
121C2×C8—182no—
122C4⋊C4—22no—
123C4⋊C4—92no—
124C4⋊C4—182no—
125C4⋊C4—182no—
126C4⋊C4C4×D912yes—
127C22⋊C4—182no—
128C42—91no—
129C42—92no—
130C42—182no—
131C42C22×D911yescharacteristic
132C22×C3D3×C22⋊C411yescharacteristic
133C2×D3—61no—
134C2×D3—62no—
135C3×C4—21no—
136C3×C4—22no—
137C3×C4—42no—
138Dic3—32no—
139Dic3—62no—
140Dic3—122no—
141C9#153711yescharacteristic, complemented, Sylow
142C23—91no—
143Q8—364no—
144C2×C4—22no—
145C2×C4—91no—
146C2×C4—92no—
147C2×C4—182no—
148C2×C4—182no—
149C2×C4—362no—
150C2×C4C2×C4×D911yescharacteristic
151C2×C4D4×D912yes—
152C8—42no—
153C8—362no—
154C2×C3D3×#10111yescharacteristic
155C2×C3#482112yes—
156D3—121no—
157C22—181no—
158C22—182no—
159C22C22⋊C4×D911yescharacteristic
160C4—21no—
161C4—22no—
162C4—42no—
163C4—92no—
164C4—182no—
165C4—362no—
166C3#6836911yescharacteristic
167C2—361no—
168C2D9×#10111yescharacteristic
169C2#1058850112yes—
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×#330C2
socleC22×C3D3×C22⋊C4
prime radicalC22×D9C22⋊C4
cosocleC42×C9C23
hypercenter#330D9
hypocenterC9#1537
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. C9×#330C2semidirect
4. #10588220C2semidirect
5. #10588141C2semidirect
66. #330D9semidirect
141. C9#1537semidirect

Maximal subgroups

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

subgroupindex
#105897902
#105883862
C9×#3302
#105882202
#105881412
#683693