Finite Group Databasebeta

← #11920103

Subgroups — #11920103

Order 1152.

447 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 447 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C23×Q8⋊C9C211yesmaximal, characteristic
2C2×#63421C212yesmaximal, complemented
3#72132—31nomaximal
4C22×Q8⋊C9—22no—
5C22×Q8⋊C9C412yescomplemented
6C22×Q8⋊C9C2211yescharacteristic
7C2×#3676—41nomaximal
8#63421—22no—
9C23×C3×Q8D311yescharacteristic
10C2×#835—32no—
11C2×#835—32no—
12#5212—31no—
13C2×#830—31no—
14C24×C9—41no—
15C22×Dic9—42no—
16C2×Q8⋊C9—22no—
17C2×Q8⋊C9C2×C411yescharacteristic
18C2×Q8⋊C9D412yes—
19#3676—44no—
20#1787—91noSylow
21C22×C3×Q8—22no—
22C22×C3×Q8—31no—
23C22×C3×Q8—32no—
24C22×C3×Q8—62no—
25C22×C3×Q8Dic312yes—
26C22×C3×Q8C2×D311yescharacteristic
27C23×C3×C4—31no—
28C2×#217—61no—
29C2×C4⋊Dic3—32no—
30C22×C3⋊C8—32no—
31#835—62no—
32#835—64no—
33#835—62no—
34C3⋊#95—61no—
35#830—62no—
36C23×C9—42no—
37C23×C9—42no—
38C23×C9—42no—
39C23×C9—41no—
40C23×C9—82no—
41C23×C9—82no—
42C2×Dic9—44no—
43C2×Dic9—82no—
44C2×Dic9—82no—
45Q8⋊C9C22⋊C411yescharacteristic, complemented
46C23×Q8D911yescharacteristic
47C2×#103—92no—
48C2×#103—92no—
49C2×C22⋊C8—91no—
50#380—91no—
51C24×C3S411yescharacteristic
52C2×C3×Q8—22no—
53C2×C3×Q8—32no—
54C2×C3×Q8—32no—
55C2×C3×Q8—31no—
56C2×C3×Q8—34no—
57C2×C3×Q8—61no—
58C2×C3×Q8—62no—
59C2×C3×Q8—64no—
60C2×C3×Q8—62no—
61C2×C3×Q8—64no—
62C2×C3×Q8C2×Dic311yescharacteristic
63C2×C3×Q8#6712yes—
64C22×C3×C4—31no—
65C22×C3×C4—32no—
66C22×C3×C4—32no—
67C22×C3×C4—31no—
68C22×C3×C4—62no—
69C22×C3×C4—62no—
70C22×Dic3—62no—
71#217—122no—
72C4⋊Dic3—62no—
73C4⋊Dic3—62no—
74C2×C3⋊C8—62no—
75C2×C3⋊C8—62no—
76C2×C3⋊C8—62no—
77C22×C9—44no—
78C22×C9—41no—
79C22×C9—41no—
80C22×C9—42no—
81C22×C9—41no—
82C22×C9—42no—
83C22×C9—82no—
84C22×C9—84no—
85C22×C9—82no—
86C22×C9—84no—
87Dic9—84no—
88C22×Q8—22no—
89C22×Q8—31no—
90C22×Q8—32no—
91C22×Q8—62no—
92C22×Q8Dic912yescomplemented
93C22×Q8C2×D911yescharacteristic
94C23×C4—31no—
95C22×C8—92no—
96C2×C4⋊C4—92no—
97C2×C22⋊C4—181no—
98#103—182no—
99#103—184no—
100#103—182no—
101C22⋊C8—182no—
102#95—181no—
103C23×C3—22no—
104C23×C3—22no—
105C23×C3#22612yes—
106C23×C3GL(2,𝔽3)12yes—
107C23×C3SL(2,ℤ/4)12yes—
108C23×C3C2×S411yescharacteristic
109C3×Q8—31no—
110C3×Q8—32no—
111C3×Q8—34no—
112C3×Q8—61no—
113C3×Q8—62no—
114C3×Q8—64no—
115C3×Q8#21711yescharacteristic
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—32no—
119C2×C3×C4—32no—
120C2×C3×C4—32no—
121C2×C3×C4—62no—
122C2×C3×C4—64no—
123C2×C3×C4—62no—
124C2×C3×C4—62no—
125C2×Dic3—122no—
126C2×Dic3—122no—
127C2×Dic3—122no—
128C3⋊C8—122no—
129C2×C9—41no—
130C2×C9—42no—
131C2×C9—41no—
132C2×C9—42no—
133C2×C9—41no—
134C2×C9—84no—
135C24(C22⋊C9)⋊C211yescharacteristic
136C2×Q8—22no—
137C2×Q8—32no—
138C2×Q8—32no—
139C2×Q8—31no—
140C2×Q8—34no—
141C2×Q8—61no—
142C2×Q8—62no—
143C2×Q8—64no—
144C2×Q8—62no—
145C2×Q8—64no—
146C2×Q8C2×Dic911yescharacteristic
147C2×Q8#61112yes—
148C22×C4—31no—
149C22×C4—32no—
150C22×C4—32no—
151C22×C4—31no—
152C22×C4—62no—
153C22×C4—62no—
154C22×C4—182no—
155C2×C8—182no—
156C2×C8—182no—
157C2×C8—182no—
158C4⋊C4—182no—
159C4⋊C4—182no—
160C22⋊C4—362no—
161C22×C3—24no—
162C22×C3—22no—
163C22×C3—24no—
164C22×C3—22no—
165C22×C3#85914yes—
166C22×C3C2×#22611yescharacteristic
167C22×C3C2×GL(2,𝔽3)11yescharacteristic
168C22×C3#98312yes—
169C22×C3C2×SL(2,ℤ/4)11yescharacteristic
170C22×C3GL(2,ℤ/4)12yes—
171C3×C4—32no—
172C3×C4—31no—
173C3×C4—31no—
174C3×C4—62no—
175Dic3—242no—
176C9—41noSylow
177C23—22no—
178C23—22no—
179C23#368812yes—
180C23#368912yes—
181C23(C22⋊C9)⋊C412yes—
182C23C2×(C22⋊C9)⋊C211yescharacteristic
183Q8—31no—
184Q8—32no—
185Q8—34no—
186Q8—61no—
187Q8—62no—
188Q8—64no—
189Q8#367611yescharacteristic, complemented
190C2×C4—31no—
191C2×C4—31no—
192C2×C4—32no—
193C2×C4—32no—
194C2×C4—32no—
195C2×C4—62no—
196C2×C4—64no—
197C2×C4—62no—
198C2×C4—62no—
199C2×C4—362no—
200C2×C4—362no—
201C2×C4—362no—
202C8—362no—
203C2×C3—24no—
204C2×C3C2×#85911yescharacteristic
205C2×C3#541912yes—
206C2×C3#542011yescharacteristic
207C2×C3#542112yes—
208C2×C3#543211yescharacteristic
209C22—24no—
210C22—22no—
211C22—24no—
212C22—22no—
213C22#6342114yescomplemented
214C22C2×#368811yescharacteristic
215C22C2×#368911yescharacteristic
216C22#6368912yes—
217C22C2×(C22⋊C9)⋊C411yescharacteristic
218C22#6369412yes—
219C4—32no—
220C4—31no—
221C4—31no—
222C4—62no—
223C4—722no—
224C3#7314811yescharacteristic
225C2—24no—
226C2C2×#6342111yescharacteristic
227C2#1058952112yes—
228C2#1058952211yescharacteristic
229C2#1058952312yes—
230C2#1058953411yescharacteristic
subgroupG/H
centerC23C2×(C22⋊C9)⋊C2
commutatorC2×Q8⋊C9C2×C4
Frattini, socleC23×C3C2×S4
FittingC23×C3×Q8D3
prime radicalC24×C3S4
cosocleC22×Q8⋊C9C22
hypercenterC24(C22⋊C9)⋊C2
hypocenterQ8⋊C9C22⋊C4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#63421C2semidirect
5. C22×Q8⋊C9C4semidirect
45. Q8⋊C9C22⋊C4semidirect
92. C22×Q8Dic9semidirect
189. Q8#3676semidirect
213. C22#63421semidirect

Maximal subgroups

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

subgroupindex
C23×Q8⋊C92
C2×#634212
#721323
C2×#36764