Finite Group Databasebeta

← C22×#131⋊C9 #11919781

Subgroups — C22×#131⋊C9 #11919781

Order 1152.

653 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 157 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
2C2×#131⋊C9C216yesmaximal, direct product factor
3C22×C3×#131C311yesmaximal, characteristic
4C2×#41⋊C9C413yes—
5C2×#41⋊C9C2213yes—
6C22×Q8⋊C9C411yescharacteristic
7C22×C8×C9—41nomaximal
8#131⋊C9C2214yesdirect product factor
9C22×C3×#41C2×C311yescharacteristic
10C2×C3×#131—36no—
11C2×C3×#131C2×C316yes—
12C22×C3×M16—31no—
13C23×C3×C8—31no—
14C22×C4×C9—41no—
15#41⋊C9C2×C413yes—
16#41⋊C9C2311yescharacteristic
17C2×Q8⋊C9C2×C413yes—
18C2×C8×C9—46no—
19C22×#131C911yescharacteristic, complemented, Sylow
20C2×C3×#41—33no—
21C2×C3×#41—33no—
22C2×C3×#41C3×C413yes—
23C2×C3×#41C22×C313yes—
24C22×C3×Q8C3×C411yescharacteristic
25C22×C3×D4—31no—
26C23×C3×C4—31no—
27C3×#131—38no—
28C3×#131—312no—
29C3×#131C22×C314yes—
30C2×C3×M16—36no—
31C2×C3×M16—36no—
32C22×C3×C8—31no—
33C22×C3×C8—36no—
34C22×C3×C8—36no—
35C22×C3×C8A411yescharacteristic
36C23×C9—41no—
37C2×C4×C9—43no—
38C2×C4×C9—43no—
39Q8⋊C9C22×C411yescharacteristic
40C8×C9—44no—
41C22×#41C2×C911yescharacteristic
42C2×#131—36no—
43C2×#131C2×C916yescomplemented
44C22×M16—31no—
45C23×C8—31no—
46C24×C3—31no—
47C3×#41—32no—
48C3×#41—36no—
49C3×#41—33no—
50C3×#41—36no—
51C3×#41—33no—
52C3×#41C2×C3×C413yes—
53C3×#41C23×C311yescharacteristic
54C2×C3×Q8—33no—
55C2×C3×Q8C2×C3×C413yes—
56C2×C3×D4—33no—
57C2×C3×D4—33no—
58C2×C3×D4—36no—
59C22×C3×C4—31no—
60C22×C3×C4—33no—
61C22×C3×C4—33no—
62C22×C3×C4—33no—
63C22×C3×C4—33no—
64C22×C3×C4C2×A411yescharacteristic
65C3×M16—312no—
66C3×M16—34no—
67C2×C3×C8—36no—
68C2×C3×C8—312no—
69C2×C3×C8—34no—
70C2×C3×C8C2×A416yes—
71C22×C9—44no—
72C22×C9—43no—
73C4×C9—43no—
74C4×C9—41no—
75C2×#41—33no—
76C2×#41—33no—
77C2×#41C4×C913yes—
78C2×#41C22×C913yes—
79C22×Q8C4×C911yescharacteristic
80C22×D4—31no—
81C23×C4—31no—
82#131—38no—
83#131—312no—
84#131C22×C914yescomplemented
85C2×M16—36no—
86C2×M16—36no—
87C22×C8—31no—
88C22×C8—36no—
89C22×C8—36no—
90C22×C8C22⋊C911yescharacteristic
91C23×C3—33no—
92C23×C3—33no—
93C23×C3—64no—
94C23×C3C4×A411yescharacteristic
95C3×Q8—33no—
96C3×Q8—32no—
97C3×Q8C22×C3×C411yescharacteristic
98C3×D4—33no—
99C3×D4—31no—
100C3×D4—36no—
101C3×D4—36no—
102C2×C3×C4—33no—
103C2×C3×C4—33no—
104C2×C3×C4—33no—
105C2×C3×C4—36no—
106C2×C3×C4—33no—
107C2×C3×C4—33no—
108C2×C3×C4—31no—
109C2×C3×C4C4×A413yes—
110C2×C3×C4C22×A413yes—
111C3×C8—34no—
112C3×C8C22×A414yes—
113C2×C9—41no—
114C2×C9—46no—
115C24—31no—
116#41—32no—
117#41—36no—
118#41—33no—
119#41—36no—
120#41—33no—
121#41C2×C4×C913yes—
122#41C23×C911yescharacteristic
123C2×Q8—33no—
124C2×Q8C2×C4×C913yes—
125C2×D4—33no—
126C2×D4—33no—
127C2×D4—36no—
128C22×C4—31no—
129C22×C4—33no—
130C22×C4—33no—
131C22×C4—33no—
132C22×C4—33no—
133C22×C4C2×C22⋊C911yescharacteristic
134M16—312no—
135M16—34no—
136C2×C8—36no—
137C2×C8—34no—
138C2×C8—312no—
139C2×C8C2×C22⋊C916yes—
140C22×C3—31no—
141C22×C3—33no—
142C22×C3—66no—
143C22×C3—66no—
144C22×C3#131⋊C314yes—
145C22×C3C2×C4×A413yes—
146C3×C4—33no—
147C3×C4—31no—
148C3×C4C2×C4×A413yes—
149C3×C4C23×A411yescharacteristic
150C9—41noSylow
151C23—33no—
152C23—33no—
153C23—64no—
154C23C4×C22⋊C911yescharacteristic
155Q8—33no—
156Q8—32no—
157Q8C22×C4×C911yescharacteristic
158D4—33no—
159D4—31no—
160D4—36no—
161D4—36no—
162C2×C4—33no—
163C2×C4—33no—
164C2×C4—31no—
165C2×C4—33no—
166C2×C4—33no—
167C2×C4—36no—
168C2×C4—33no—
169C2×C4C4×C22⋊C913yes—
170C2×C4C22×C22⋊C913yes—
171C8—34no—
172C8C22×C22⋊C914yes—
173C2×C3—61no—
174C2×C3—63no—
175C2×C3C2×#131⋊C316yes—
176C2×C3C22×C4×A411yescharacteristic
177C22—31no—
178C22—33no—
179C22—66no—
180C22—66no—
181C22#131⋊C914yesdirect product factor
182C22C2×C4×C22⋊C913yes—
183C4—31no—
184C4—33no—
185C4C2×C4×C22⋊C913yes—
186C4C23×C22⋊C911yescharacteristic
187C3C22×#131⋊C311yescharacteristic
188C2—61no—
189C2—63no—
190C2C2×#131⋊C916yesdirect product factor
191C2C22×C4×C22⋊C911yescharacteristic
subgroupG/H
center, hypercenterC22×C3×C8A4
commutator, hypocenterQ8C22×C4×C9
FrattiniC3×C4C23×A4
FittingC22×C3×#131C3
socleC23×C3C4×A4
prime radicalC22×C3×#41C2×C3
cosocleC3×#41C23×C3
LCSG ▷ Q8
UCSC1 ◁ C22×C3×C8

Complements

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

NH ≅ G/Ntype
2. C2×#131⋊C9C2direct (N × H)
8. #131⋊C9C22direct (N × H)
19. C22×#131C9semidirect
43. C2×#131C2×C9semidirect
84. #131C22×C9semidirect
181. C22#131⋊C9direct (N × H)
190. C2C2×#131⋊C9direct (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
C2×#131⋊C92
C22×C3×#1313
C22×C8×C94