Finite Group Databasebeta

← C2×#10589528 #11920417

Subgroups — C2×#10589528 #11920417

Order 1152.

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

normal subgroups only

This group has 621 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
1C22×#41⋊C9C211yesmaximal, characteristic
2#10589528C214yesmaximal, direct product factor
3C2×#63421C212yesmaximal, complemented
4C2×#5232—31nomaximal
5C2×#41⋊C9C414yescomplemented
6C2×#41⋊C9C2212yes—
7C22×Q8⋊C9C2211yescharacteristic
8C2×C4⋊Dic9—41nomaximal
9#63421C2214yescomplemented
10C22×C3×#41D311yescharacteristic
11C22×C4⋊Dic3—31no—
12C22×#208—31no—
13#5232—34no—
14#5232—34no—
15C2×#835—32no—
16C2×#832—32no—
17C22×C4×C9—41no—
18C22×Dic9—42no—
19#41⋊C9C2×C414yescomplemented
20C2×Q8⋊C9C2×C412yescomplemented
21C2×Q8⋊C9C2311yescharacteristic
22C4⋊Dic9—44no—
23C2×#417—91noSylow
24C2×C3×#41—34no—
25C2×C3×#41—32no—
26C2×C3×#41Dic314yes—
27C2×C3×#41C2×D312yes—
28C22×C3×Q8C2×D311yescharacteristic
29C22×C3×D4—31no—
30C23×C3×C4—31no—
31C23×Dic3—61no—
32C2×C4⋊Dic3—32no—
33C2×C4⋊Dic3—34no—
34C2×C4⋊Dic3—62no—
35C2×C4⋊Dic3—61no—
36C2×#208—34no—
37C2×#208—64no—
38C22×C3⋊C8—32no—
39#835—34no—
40#835—34no—
41#832—38no—
42C23×C9—41no—
43C2×C4×C9—44no—
44C2×C4×C9—42no—
45C2×Dic9—44no—
46C2×Dic9—84no—
47Q8⋊C9C22×C411yescharacteristic, complemented
48C22×#41D911yescharacteristic
49C22×M16—91no—
50C22×C4⋊C4—91no—
51#417—94no—
52#417—94no—
53C2×#103—92no—
54C2×#102—92no—
55C24×C3—31no—
56C3×#41—38no—
57C3×#41—34no—
58C3×#41—64no—
59C3×#41C2×Dic314yes—
60C2×C3×Q8—31no—
61C2×C3×Q8—32no—
62C2×C3×Q8C2×Dic312yes—
63C2×C3×Q8C22×D311yescharacteristic
64C2×C3×D4—32no—
65C2×C3×D4—34no—
66C2×C3×D4—62no—
67C2×C3×D4—61no—
68C22×C3×C4—31no—
69C22×C3×C4—34no—
70C22×C3×C4—34no—
71C22×C3×C4—32no—
72C22×C3×C4—32no—
73C22×C3×C4S411yescharacteristic
74C22×Dic3—64no—
75C22×Dic3—62no—
76C22×Dic3—124no—
77C4⋊Dic3—34no—
78C4⋊Dic3—62no—
79C4⋊Dic3—64no—
80#208—68no—
81C2×C3⋊C8—34no—
82C2×C3⋊C8—64no—
83C22×C9—42no—
84C22×C9—42no—
85C22×C9—42no—
86C22×C9—41no—
87C4×C9—44no—
88Dic9—84no—
89C2×#41—32no—
90C2×#41—34no—
91C2×#41Dic914yescomplemented
92C2×#41C2×D912yes—
93C22×Q8C2×D911yescharacteristic
94C22×D4—31no—
95C23×C4—31no—
96C23×C4—181no—
97C2×M16—94no—
98C2×M16—184no—
99C22×C8—92no—
100C2×C4⋊C4—92no—
101C2×C4⋊C4—94no—
102C2×C4⋊C4—182no—
103C2×C4⋊C4—181no—
104#103—94no—
105#103—94no—
106#102—98no—
107C23×C3—34no—
108C23×C3—32no—
109C23×C3—62no—
110C23×C3—62no—
111C23×C3C2×S411yescharacteristic
112C3×Q8—32no—
113C3×Q8—31no—
114C3×Q8—61no—
115C3×Q8C22×Dic311yescharacteristic
116C3×D4—34no—
117C3×D4—62no—
118C3×D4—64no—
119C2×C3×C4—32no—
120C2×C3×C4—32no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—34no—
124C2×C3×C4—34no—
125C2×C3×C4—38no—
126C2×C3×C4SL(2,ℤ/4)14yes—
127C2×C3×C4C2×S412yes—
128C2×Dic3—64no—
129C2×Dic3—128no—
130C2×Dic3—124no—
131C3⋊C8—64no—
132C2×C9—41no—
133C2×C9—41no—
134C2×C9—41no—
135C2×C9—44no—
136C24—31no—
137#41—38no—
138#41—34no—
139#41—64no—
140#41C2×Dic914yescomplemented
141C2×Q8—31no—
142C2×Q8—32no—
143C2×Q8C2×Dic912yes—
144C2×Q8C22×D911yescharacteristic
145C2×D4—32no—
146C2×D4—34no—
147C2×D4—61no—
148C2×D4—62no—
149C22×C4—31no—
150C22×C4—34no—
151C22×C4—34no—
152C22×C4—32no—
153C22×C4—32no—
154C22×C4—184no—
155C22×C4—182no—
156C22×C4—364no—
157C22×C4(C22⋊C9)⋊C211yescharacteristic
158M16—188no—
159C2×C8—94no—
160C2×C8—184no—
161C4⋊C4—94no—
162C4⋊C4—182no—
163C4⋊C4—184no—
164C22×C3—34no—
165C22×C3—62no—
166C22×C3—62no—
167C22×C3—68no—
168C22×C3#98412yes—
169C22×C3#98612yes—
170C22×C3C2×SL(2,ℤ/4)12yes—
171C22×C3C22×S411yescharacteristic
172C3×C4—31no—
173C3×C4—31no—
174C3×C4—32no—
175C3×C4C2×SL(2,ℤ/4)14yes—
176Dic3—124no—
177C9—41noSylow
178C23—32no—
179C23—34no—
180C23—62no—
181C23—62no—
182C23C2×(C22⋊C9)⋊C211yescharacteristic
183Q8—32no—
184Q8—31no—
185Q8—61no—
186Q8C22×Dic911yescharacteristic
187D4—34no—
188D4—62no—
189D4—64no—
190C2×C4—31no—
191C2×C4—31no—
192C2×C4—32no—
193C2×C4—32no—
194C2×C4—34no—
195C2×C4—34no—
196C2×C4—38no—
197C2×C4—184no—
198C2×C4—368no—
199C2×C4—364no—
200C2×C4(C22⋊C9)⋊C414yes—
201C2×C4C2×(C22⋊C9)⋊C212yes—
202C8—184no—
203C2×C3—64no—
204C2×C3#542614yes—
205C2×C3C2×#98411yescharacteristic
206C2×C3C2×#98611yescharacteristic
207C2×C3C22×SL(2,ℤ/4)11yescharacteristic
208C22—34no—
209C22—62no—
210C22—62no—
211C22—68no—
212C22#6369012yes—
213C22#6369212yes—
214C22C2×(C22⋊C9)⋊C412yes—
215C22C22×(C22⋊C9)⋊C211yescharacteristic
216C4—31no—
217C4—31no—
218C4—32no—
219C4—364no—
220C4C2×(C22⋊C9)⋊C414yes—
221C3C2×#542611yescharacteristic
222C2—64no—
223C2#1058952814yesdirect product factor
224C2C2×#6369011yescharacteristic
225C2C2×#6369211yescharacteristic
226C2C22×(C22⋊C9)⋊C411yescharacteristic
subgroupG/H
centerC23C2×(C22⋊C9)⋊C2
commutator, hypocenterQ8⋊C9C22×C4
FrattiniC22×C3C22×S4
Fitting, prime radicalC22×C3×#41D3
socleC23×C3C2×S4
cosocleC2×Q8⋊C9C23
hypercenterC22×C4(C22⋊C9)⋊C2
LCSG ▷ Q8⋊C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10589528C2direct (N × H)
3. C2×#63421C2semidirect
5. C2×#41⋊C9C4semidirect
9. #63421C22semidirect
19. #41⋊C9C2×C4semidirect
20. C2×Q8⋊C9C2×C4semidirect
47. Q8⋊C9C22×C4semidirect
91. C2×#41Dic9semidirect
140. #41C2×Dic9semidirect
223. C2#10589528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
#105895282
C2×#634212
C2×#52323
C2×C4⋊Dic94