Finite Group Databasebeta

← #11920041

Subgroups — #11920041

Order 1152.

193 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 193 conjugacy classes of subgroups — too many to draw. Only its 37 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
1D4×Q8⋊C9C211yesmaximal, characteristic
2#10589493C211yesmaximal, characteristic, complemented
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic, complemented
4#71915—31nomaximal
5C22×Q8⋊C9—21no—
6C4×Q8⋊C9C2211yescharacteristic
7#63421—21no—
8#63392—41nomaximal
9C3×D4×Q8D311yescharacteristic
10#5093—31no—
11#5021—31no—
12#5008—31no—
13#4547—31no—
14#4535—31no—
15D4⋊(C3⋊C8)—31no—
16C2×D4×C9—41no—
17C2×Q8⋊C9—41no—
18C2×Q8⋊C9D411yescharacteristic
19C4⋊Dic9—41no—
20C2×C9⋊C8—41no—
21#1637—91noSylow
22C22×C3×Q8—21no—
23C3×C4⋊Q8—31no—
24C3×C22⋊Q8—61no—
25C3×C4×Q8C2×D311yescharacteristic
26C3×C4×D4—31no—
27#869—31no—
28#835—61no—
29#832—61no—
30#810—62no—
31#808—61no—
32#807—61no—
33C4⋊(C3⋊C8)—31no—
34C4⋊(C3⋊C8)—31no—
35C4×C3⋊C8—31no—
36C23×C9—81no—
37D4×C9—42no—
38D4×C9—81no—
39C2×C4×C9—41no—
40C2×Dic9—81no—
41Q8⋊C9SD1611yescharacteristic
42C9⋊C8—81no—
43D4×Q8D911yescharacteristic
44#487—91no—
45#477—91no—
46#476—91no—
47#332—91no—
48Q8⋊C8—91no—
49D4⋊C8—91no—
50C2×C3×Q8—41no—
51C2×C3×Q8—61no—
52C2×C3×Q8—121no—
53C2×C3×Q8#6711yescharacteristic
54C2×C3×D4S411yescharacteristic
55C22×C3×C4—61no—
56C2×Dic6—61no—
57C3×C4⋊C4—31no—
58C3×C4⋊C4—32no—
59C3×C4⋊C4—31no—
60C3×C22⋊C4—61no—
61C3×C42—31no—
62C4⋊Dic3—61no—
63C4⋊Dic3—61no—
64C2×C3⋊C8—61no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67C22×C9—41no—
68C22×C9—82no—
69C22×C9—161no—
70C22×C9—161no—
71C4×C9—41no—
72C4×C9—41no—
73Dic9—161no—
74C22×Q8—21no—
75C4⋊Q8—31no—
76C4⋊Q8—91no—
77C22⋊Q8—61no—
78C4×Q8C2×D911yescharacteristic
79C4×D4—31no—
80#107—181no—
81#106—181no—
82C4⋊C8—91no—
83C4⋊C8—91no—
84#103—182no—
85#103—181no—
86#102—181no—
87C4×C8—91no—
88C23×C3—21no—
89C3×Q8—31no—
90C3×Q8—121no—
91C3×Q8—121no—
92C3×Q8#21411yescharacteristic
93C3×D4—21no—
94C3×D4#22612yes—
95C2×C3×C4—31no—
96C2×C3×C4—31no—
97C2×C3×C4—61no—
98C2×C3×C4—121no—
99C2×C3×C4—121no—
100C2×C3×C4C2×S411yescharacteristic
101C2×Dic3—121no—
102Dic6—122no—
103C3⋊C8—121no—
104C3⋊C8—121no—
105C3⋊C8—121no—
106C2×C9—41no—
107C2×C9—41no—
108C2×C9—41no—
109C2×C9—162no—
110C2×Q8—41no—
111C2×Q8—61no—
112C2×Q8—121no—
113C2×Q8—181no—
114C2×Q8#61111yescharacteristic
115C2×D4(C22⋊C9)⋊C211yescharacteristic
116C22×C4—61no—
117C2×C8—181no—
118C2×C8—181no—
119C2×C8—181no—
120C4⋊C4—31no—
121C4⋊C4—32no—
122C4⋊C4—31no—
123C4⋊C4—181no—
124C4⋊C4—181no—
125C22⋊C4—61no—
126C42—31no—
127C22×C3—22no—
128C22×C3—41no—
129C22×C3—41no—
130C22×C3GL(2,ℤ/4)11yescharacteristic
131C3×C4—31no—
132C3×C4—31no—
133C3×C4—61no—
134C3×C4—121no—
135C3×C4C2×#22611yescharacteristic
136C3×C4#98311yescharacteristic
137Dic3—241no—
138C9—41noSylow
139C23—21no—
140Q8—31no—
141Q8—121no—
142Q8—121no—
143Q8—362no—
144Q8#367211yescharacteristic
145D4—21no—
146D4#368812yes—
147C2×C4—31no—
148C2×C4—31no—
149C2×C4—61no—
150C2×C4—121no—
151C2×C4—121no—
152C2×C4—361no—
153C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
154C8—361no—
155C8—361no—
156C8—361no—
157C2×C3—42no—
158C2×C3#541411yescharacteristic
159C2×C3#541911yescharacteristic
160C2×C3#543111yescharacteristic
161C22—22no—
162C22—41no—
163C22—41no—
164C22#6369411yescharacteristic
165C4—31no—
166C4—31no—
167C4—61no—
168C4—121no—
169C4—721no—
170C4C2×#368811yescharacteristic
171C4#6368911yescharacteristic
172C3#7308611yescharacteristic
173C2—42no—
174C2#1058951611yescharacteristic
175C2#1058952111yescharacteristic
176C2#1058953311yescharacteristic
subgroupG/H
centerC22#63694
commutator, cosocleC4×Q8⋊C9C22
FrattiniC2×C3×C4C2×S4
FittingC3×D4×Q8D3
socleC22×C3GL(2,ℤ/4)
prime radicalC2×C3×D4S4
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterQ8⋊C9SD16
LCSG ▷ C4×Q8⋊C9 ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10589493C2semidirect
3. (Q8⋊C9)⋊C8C2semidirect

Maximal subgroups

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

subgroupindex
D4×Q8⋊C92
#105894932
(Q8⋊C9)⋊C82
#719153
#633924