Finite Group Databasebeta

← C2×#10589522 #11920402

Subgroups — C2×#10589522 #11920402

Order 1152.

617 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 617 conjugacy classes of subgroups — too many to draw. Only its 113 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
2#10589522C214yesmaximal, direct product factor
3C2×#63421C212yesmaximal, complemented
4C2×#5225—31nomaximal
5C22×Q8⋊C9C414yescomplemented
6C22×Q8⋊C9C2211yescharacteristic
7C22×Q8⋊C9C2212yes—
8C2×#3676—41nomaximal
9#63421C2214yescomplemented
10C23×C3×Q8D311yescharacteristic
11C2×#926—31no—
12C22×#208—31no—
13#5225—34no—
14#5225—34no—
15C2×#835—32no—
16C2×#835—32no—
17C24×C9—41no—
18C22×Dic9—42no—
19C2×Q8⋊C9C2×C412yes—
20C2×Q8⋊C9C2×C414yescomplemented
21C2×Q8⋊C9C2311yescharacteristic
22#3676—44no—
23C2×#419—91noSylow
24C22×C3×Q8—34no—
25C22×C3×Q8—31no—
26C22×C3×Q8—32no—
27C22×C3×Q8Dic314yes—
28C22×C3×Q8C2×D311yescharacteristic
29C22×C3×Q8C2×D312yes—
30C23×C3×C4—31no—
31C2×#217—61no—
32#926—34no—
33#926—62no—
34C2×C4⋊Dic3—32no—
35C2×C4×Dic3—61no—
36C2×#208—34no—
37C2×#208—64no—
38C22×C3⋊C8—32no—
39#835—38no—
40#835—34no—
41#835—34no—
42C23×C9—44no—
43C23×C9—41no—
44C23×C9—42no—
45C23×C9—84no—
46C2×Dic9—44no—
47C2×Dic9—84no—
48Q8⋊C9C22×C411yescharacteristic
49C23×Q8D911yescharacteristic
50C22×M16—91no—
51C2×#117—91no—
52#419—94no—
53#419—94no—
54C2×#103—92no—
55C2×#103—92no—
56C24×C3S411yescharacteristic
57C2×C3×Q8—32no—
58C2×C3×Q8—31no—
59C2×C3×Q8—34no—
60C2×C3×Q8—38no—
61C2×C3×Q8—32no—
62C2×C3×Q8—34no—
63C2×C3×Q8—62no—
64C2×C3×Q8—64no—
65C2×C3×Q8—61no—
66C2×C3×Q8C2×Dic312yes—
67C2×C3×Q8C2×Dic314yes—
68C2×C3×Q8C22×D311yescharacteristic
69C22×C3×C4—34no—
70C22×C3×C4—34no—
71C22×C3×C4—31no—
72C22×C3×C4—32no—
73C22×C3×C4—31no—
74C22×C3×C4—32no—
75C22×Dic3—62no—
76#217—64no—
77C4⋊Dic3—34no—
78C4⋊Dic3—62no—
79C4×Dic3—64no—
80#208—68no—
81C2×C3⋊C8—34no—
82C2×C3⋊C8—64no—
83C22×C9—44no—
84C22×C9—42no—
85C22×C9—44no—
86C22×C9—41no—
87C22×C9—84no—
88C22×C9—88no—
89Dic9—84no—
90C22×Q8—31no—
91C22×Q8—32no—
92C22×Q8—34no—
93C22×Q8Dic914yescomplemented
94C22×Q8C2×D911yescharacteristic
95C22×Q8C2×D912yes—
96C23×C4—31no—
97C2×M16—94no—
98C2×M16—184no—
99C22×C8—92no—
100#117—94no—
101#117—182no—
102C2×C4⋊C4—92no—
103C2×C22⋊C4—181no—
104C2×C42—181no—
105#103—98no—
106#103—94no—
107#103—94no—
108C23×C3—24no—
109C23×C3SL(2,ℤ/4)14yes—
110C23×C3C2×S412yes—
111C23×C3C2×S411yescharacteristic
112C3×Q8—32no—
113C3×Q8—34no—
114C3×Q8—31no—
115C3×Q8—61no—
116C3×Q8—62no—
117C3×Q8—64no—
118C3×Q8C22×Dic311yescharacteristic
119C2×C3×C4—32no—
120C2×C3×C4—34no—
121C2×C3×C4—32no—
122C2×C3×C4—34no—
123C2×C3×C4—38no—
124C2×C3×C4—34no—
125C2×C3×C4—31no—
126C2×C3×C4—32no—
127C2×C3×C4—31no—
128C2×Dic3—64no—
129C2×Dic3—124no—
130C3⋊C8—64no—
131C2×C9—42no—
132C2×C9—41no—
133C2×C9—44no—
134C2×C9—84no—
135C24(C22⋊C9)⋊C211yescharacteristic
136C2×Q8—32no—
137C2×Q8—31no—
138C2×Q8—34no—
139C2×Q8—38no—
140C2×Q8—32no—
141C2×Q8—34no—
142C2×Q8—61no—
143C2×Q8—62no—
144C2×Q8—64no—
145C2×Q8C2×Dic912yes—
146C2×Q8C2×Dic914yescomplemented
147C2×Q8C22×D911yescharacteristic
148C22×C4—34no—
149C22×C4—34no—
150C22×C4—32no—
151C22×C4—32no—
152C22×C4—31no—
153C22×C4—31no—
154C22×C4—182no—
155M16—188no—
156C2×C8—94no—
157C2×C8—184no—
158C4⋊C4—94no—
159C4⋊C4—182no—
160C22⋊C4—184no—
161C42—184no—
162C22×C3—24no—
163C22×C3—28no—
164C22×C3#98314yes—
165C22×C3C2×SL(2,ℤ/4)14yes—
166C22×C3C2×SL(2,ℤ/4)12yes—
167C22×C3C22×S411yescharacteristic
168C3×C4—31no—
169C3×C4—31no—
170C3×C4—32no—
171C3×C4—34no—
172Dic3—124no—
173C9—41noSylow
174C23—24no—
175C23(C22⋊C9)⋊C414yes—
176C23C2×(C22⋊C9)⋊C212yes—
177C23C2×(C22⋊C9)⋊C211yescharacteristic
178Q8—32no—
179Q8—34no—
180Q8—31no—
181Q8—62no—
182Q8—61no—
183Q8—64no—
184Q8C22×Dic911yescharacteristic
185C2×C4—32no—
186C2×C4—31no—
187C2×C4—31no—
188C2×C4—32no—
189C2×C4—34no—
190C2×C4—32no—
191C2×C4—34no—
192C2×C4—38no—
193C2×C4—34no—
194C2×C4—184no—
195C2×C4—364no—
196C8—184no—
197C2×C3—24no—
198C2×C3#542014yes—
199C2×C3C2×#98312yes—
200C2×C3C22×SL(2,ℤ/4)11yescharacteristic
201C22—24no—
202C22—28no—
203C22#6368914yes—
204C22C2×(C22⋊C9)⋊C414yes—
205C22C2×(C22⋊C9)⋊C412yes—
206C22C22×(C22⋊C9)⋊C211yescharacteristic
207C4—31no—
208C4—31no—
209C4—34no—
210C4—32no—
211C4—364no—
212C3C2×#542011yescharacteristic
213C2—24no—
214C2#1058952214yesdirect product factor
215C2C2×#6368912yes—
216C2C22×(C22⋊C9)⋊C411yescharacteristic
subgroupG/H
centerC23C2×(C22⋊C9)⋊C2
commutator, hypocenterQ8⋊C9C22×C4
FrattiniC22×C3C22×S4
FittingC23×C3×Q8D3
socleC23×C3C2×S4
prime radicalC24×C3S4
cosocleC2×Q8⋊C9C23
hypercenterC24(C22⋊C9)⋊C2
LCSG ▷ Q8⋊C9
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. #10589522C2direct (N × H)
3. C2×#63421C2semidirect
5. C22×Q8⋊C9C4semidirect
9. #63421C22semidirect
20. C2×Q8⋊C9C2×C4semidirect
93. C22×Q8Dic9semidirect
146. C2×Q8C2×Dic9semidirect
214. C2#10589522direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8⋊C92
#105895222
C2×#634212
C2×#52253
C2×#36764