Finite Group Databasebeta

← #11920040

Subgroups — #11920040

Order 1152.

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

normal subgroups only

This group has 200 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
2C4⋊#3688C211yesmaximal, characteristic, complemented
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic, complemented
4#71916—31nomaximal
5C22×Q8⋊C9—21no—
6C2×#3688—21no—
7C4×Q8⋊C9C2211yescharacteristic
8#63392—41nomaximal
9C3×D4×Q8D311yescharacteristic
10#5078—31no—
11#5031—31no—
12#5007—31no—
13#4547—31no—
14#4535—31no—
15D4⋊(C3⋊C8)—31no—
16C2×D4×C9—41no—
17C2×Q8⋊C9—41no—
18C2×Q8⋊C9D411yescharacteristic
19#3688—41no—
20C4⋊Dic9—41no—
21C2×C9⋊C8—41no—
22#1649—91noSylow
23C22×C3×Q8—21no—
24C3×C4⋊Q8—31no—
25C3×C22⋊Q8—61no—
26C3×C4×Q8C2×D311yescharacteristic
27C3×C4×D4—31no—
28C2×#216—61no—
29#869—31no—
30#832—61no—
31#810—61no—
32#807—61no—
33#807—62no—
34C4⋊(C3⋊C8)—31no—
35C4⋊(C3⋊C8)—31no—
36C4×C3⋊C8—31no—
37C23×C9—81no—
38D4×C9—42no—
39D4×C9—81no—
40C2×C4×C9—41no—
41C2×Dic9—81no—
42Q8⋊C9D811yescharacteristic
43C9⋊C8—81no—
44D4×Q8D911yescharacteristic
45#500—91no—
46#474—91no—
47#462—91no—
48#332—91no—
49Q8⋊C8—91no—
50D4⋊C8—91no—
51C2×C3×Q8—41no—
52C2×C3×Q8—61no—
53C2×C3×Q8—121no—
54C2×C3×Q8#6711yescharacteristic
55C2×C3×D4S411yescharacteristic
56C22×C3×C4—61no—
57C2×Dic6—61no—
58C3×C4⋊C4—31no—
59C3×C4⋊C4—32no—
60C3×C4⋊C4—31no—
61C3×C22⋊C4—61no—
62C3×C42—31no—
63#216—121no—
64#216—121no—
65C4⋊Dic3—61no—
66C4⋊Dic3—61no—
67C2×C3⋊C8—61no—
68C2×C3⋊C8—61no—
69C2×C3⋊C8—61no—
70C22×C9—41no—
71C22×C9—82no—
72C22×C9—161no—
73C22×C9—161no—
74C4×C9—41no—
75C4×C9—41no—
76Dic9—161no—
77C22×Q8—21no—
78C2×Q16—181no—
79C4⋊Q8—31no—
80C4⋊Q8—91no—
81C22⋊Q8—61no—
82C4×Q8C2×D911yescharacteristic
83C4×D4—31no—
84#107—181no—
85#107—182no—
86C4⋊C8—91no—
87C4⋊C8—91no—
88#103—181no—
89#102—181no—
90C4×C8—91no—
91C23×C3—21no—
92C3×Q8—31no—
93C3×Q8—121no—
94C3×Q8—121no—
95C3×Q8#21311yescharacteristic
96C3×D4—21no—
97C3×D4#22612yes—
98C2×C3×C4—31no—
99C2×C3×C4—31no—
100C2×C3×C4—61no—
101C2×C3×C4—121no—
102C2×C3×C4—121no—
103C2×C3×C4C2×S411yescharacteristic
104C2×Dic3—121no—
105Dic6—121no—
106Dic6—121no—
107C3⋊C8—62no—
108C3⋊C8—121no—
109C3⋊C8—121no—
110C2×C9—41no—
111C2×C9—41no—
112C2×C9—41no—
113C2×C9—162no—
114C2×Q8—41no—
115C2×Q8—61no—
116C2×Q8—121no—
117C2×Q8—181no—
118C2×Q8#61111yescharacteristic
119C2×D4(C22⋊C9)⋊C211yescharacteristic
120C22×C4—61no—
121Q16—361no—
122Q16—361no—
123C2×C8—181no—
124C2×C8—181no—
125C2×C8—181no—
126C4⋊C4—31no—
127C4⋊C4—32no—
128C4⋊C4—31no—
129C4⋊C4—181no—
130C4⋊C4—181no—
131C22⋊C4—61no—
132C42—31no—
133C22×C3—22no—
134C22×C3—41no—
135C22×C3—41no—
136C22×C3GL(2,ℤ/4)11yescharacteristic
137C3×C4—31no—
138C3×C4—31no—
139C3×C4—61no—
140C3×C4—121no—
141C3×C4C2×#22611yescharacteristic
142C3×C4#98311yescharacteristic
143Dic3—241no—
144C9—41noSylow
145C23—21no—
146Q8—31no—
147Q8—121no—
148Q8—121no—
149Q8—361no—
150Q8—361no—
151Q8#367311yescharacteristic
152D4—21no—
153D4#368812yescomplemented
154C2×C4—31no—
155C2×C4—31no—
156C2×C4—61no—
157C2×C4—121no—
158C2×C4—121no—
159C2×C4—361no—
160C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
161C8—182no—
162C8—361no—
163C8—361no—
164C2×C3—42no—
165C2×C3#541511yescharacteristic
166C2×C3#541911yescharacteristic
167C2×C3#543011yescharacteristic
168C22—22no—
169C22—41no—
170C22—41no—
171C22#6369411yescharacteristic
172C4—31no—
173C4—31no—
174C4—61no—
175C4—121no—
176C4—721no—
177C4C2×#368811yescharacteristic
178C4#6368911yescharacteristic
179C3#7308511yescharacteristic
180C2—42no—
181C2#1058951711yescharacteristic
182C2#1058952111yescharacteristic
183C2#1058953211yescharacteristic
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⋊C9D8
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. C4⋊#3688C2semidirect
3. (Q8⋊C9)⋊C8C2semidirect
153. D4#3688semidirect

Maximal subgroups

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

subgroupindex
D4×Q8⋊C92
C4⋊#36882
(Q8⋊C9)⋊C82
#719163
#633924