Finite Group Databasebeta

← C32×#1345 #11768394

Subgroups — C32×#1345 #11768394

Order 1152.

504 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C32×#394C211yesmaximal, characteristic
2C32×#343C211yesmaximal, characteristic, complemented
3C32×#324C211yesmaximal, characteristic, complemented
4C3×#1345C314yesmaximal, direct product factor
5C22×C32×D4C411yescharacteristic
6C2×C32×M16—21no—
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4—21no—
10C32×C22⋊C8—21no—
11C32×#95C411yescharacteristic
12C3×#394C2×C314yes—
13C3×#343C2×C314yescomplemented
14C3×#324C2×C314yescomplemented
15C24×C32—21no—
16C2×C32×D4—41no—
17C2×C32×D4—42no—
18C22×C32×C4—21no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4D411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C32×M16—22no—
23C32×M16—41no—
24C2×C32×C8—41no—
25C2×C32×C8—41no—
26C32×C4⋊C4—41no—
27C32×C22⋊C4—42no—
28C32×C22⋊C4—41no—
29C32×C22⋊C4—41no—
30#1345C3211yescharacteristic, direct product factor, Sylow
31C22×C3×D4C3×C414yes—
32C2×C3×M16—24no—
33C2×C3×C4⋊C4C22×C314yes—
34C2×C3×C22⋊C4—24no—
35C2×C3×C22⋊C4—24no—
36C3×C22⋊C8—24no—
37C3×#95C3×C414yes—
38C23×C32—22no—
39C23×C32—41no—
40C23×C32—41no—
41C23×C32—41no—
42C23×C32—41no—
43C23×C32—41no—
44C23×C32—41no—
45C23×C32C22⋊C411yescharacteristic
46C32×D4—42no—
47C32×D4—42no—
48C2×C32×C4—21no—
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—41no—
53C2×C32×C4—41no—
54C2×C32×C4—41no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4D811yescharacteristic
58C2×C32×C4SD1611yescharacteristic
59C32×C8—42no—
60C32×C8—81no—
61#394C2×C3211yescharacteristic
62#343C2×C3211yescharacteristic, complemented
63#324C2×C3211yescharacteristic, complemented
64C24×C3—24no—
65C2×C3×D4—44no—
66C2×C3×D4—48no—
67C22×C3×C4—24no—
68C22×C3×C4C2×C3×C414yes—
69C22×C3×C4C3×D414yes—
70C22×C3×C4C3×D414yes—
71C3×M16—28no—
72C3×M16—44no—
73C2×C3×C8—44no—
74C2×C3×C8—44no—
75C3×C4⋊C4—44no—
76C3×C22⋊C4—48no—
77C3×C22⋊C4—44no—
78C3×C22⋊C4—44no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32—42no—
82C22×C32—42no—
83C22×C32—42no—
84C22×C32—81no—
85C22×C32—81no—
86C22×C32—81no—
87C22×C32—81no—
88C22×C32#9911yescharacteristic
89C22×C32#10211yescharacteristic
90C22×C32#10411yescharacteristic
91C32×C4—21no—
92C32×C4—21no—
93C32×C4—41no—
94C32×C4—41no—
95C32×C4—81no—
96C22×D4C32×C411yescharacteristic
97C2×M16—21no—
98C2×C4⋊C4C22×C3211yescharacteristic
99C2×C22⋊C4—21no—
100C2×C22⋊C4—21no—
101C22⋊C8—21no—
102#95C32×C411yescharacteristic
103C23×C3—28no—
104C23×C3—44no—
105C23×C3—44no—
106C23×C3—44no—
107C23×C3—44no—
108C23×C3—44no—
109C23×C3—44no—
110C23×C3C3×C22⋊C414yes—
111C3×D4—48no—
112C3×D4—48no—
113C2×C3×C4—24no—
114C2×C3×C4—24no—
115C2×C3×C4—24no—
116C2×C3×C4—24no—
117C2×C3×C4—44no—
118C2×C3×C4—44no—
119C2×C3×C4—44no—
120C2×C3×C4—44no—
121C2×C3×C4—44no—
122C2×C3×C4C3×D814yes—
123C2×C3×C4C3×SD1614yes—
124C3×C8—48no—
125C3×C8—84no—
126C2×C32—21no—
127C2×C32—21no—
128C2×C32—82no—
129C2×C32#32711yescharacteristic
130C2×C32AΣL(1,𝔽16)11yescharacteristic
131C2×C32#35511yescharacteristic
132C24—21no—
133C2×D4—41no—
134C2×D4—42no—
135C22×C4—21no—
136C22×C4C2×C32×C411yescharacteristic
137C22×C4C32×D411yescharacteristic
138C22×C4C32×D411yescharacteristic
139M16—22no—
140M16—41no—
141C2×C8—41no—
142C2×C8—41no—
143C4⋊C4—41no—
144C22⋊C4—42no—
145C22⋊C4—41no—
146C22⋊C4—41no—
147C22×C3—24no—
148C22×C3—24no—
149C22×C3—48no—
150C22×C3—48no—
151C22×C3—48no—
152C22×C3—84no—
153C22×C3—84no—
154C22×C3—84no—
155C22×C3—84no—
156C22×C3C3×#9914yes—
157C22×C3C3×#10214yes—
158C22×C3C3×#10414yes—
159C3×C4—24no—
160C3×C4—24no—
161C3×C4—44no—
162C3×C4—44no—
163C3×C4—84no—
164C32#134511yescharacteristic, direct product factor, Sylow
165C23—22no—
166C23—41no—
167C23—41no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23—41no—
172C23C32×C22⋊C411yescharacteristic
173D4—42no—
174D4—42no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4C32×D811yescharacteristic
185C2×C4C32×SD1611yescharacteristic
186C8—42no—
187C8—81no—
188C2×C3—24no—
189C2×C3—24no—
190C2×C3—88no—
191C2×C3C3×#32714yes—
192C2×C3C3×AΣL(1,𝔽16)14yes—
193C2×C3C3×#35514yes—
194C22—21no—
195C22—21no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—81no—
203C22C32×#9911yescharacteristic
204C22C32×#10211yescharacteristic
205C22C32×#10411yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C3C3×#134514yesdirect product factor
212C2—21no—
213C2—21no—
214C2—82no—
215C2C32×#32711yescharacteristic
216C2C32×AΣL(1,𝔽16)11yescharacteristic
217C2C32×#35511yescharacteristic
subgroupG/H
center, socleC22×C32#99
commutatorC22×C4C2×C32×C4
Frattini, cosocleC2×C4⋊C4C22×C32
prime radicalC22×C32×D4C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C23×C32 ◁ C2×C32×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×#343C2semidirect
3. C32×#324C2semidirect
4. C3×#1345C3direct (N × H)
13. C3×#343C2×C3semidirect
14. C3×#324C2×C3semidirect
30. #1345C32direct (N × H)
62. #343C2×C32semidirect
63. #324C2×C32semidirect
164. C32#1345direct (N × H)
211. C3C3×#1345direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#3942
C32×#3432
C32×#3242
C3×#13453