Finite Group Databasebeta

← C32×#1352 #11768401

Subgroups — C32×#1352 #11768401

Order 1152.

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

normal subgroups only

This group has 462 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×#399C211yesmaximal, characteristic
2C32×#342C211yesmaximal, characteristic
3C32×#323C211yesmaximal, characteristic
4C3×#1352C314yesmaximal, direct product factor
5C2×C32×C4⋊C4—21no—
6C2×C32×C4⋊C4C411yescharacteristic, complemented
7C2×C32×C22⋊C4—21no—
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4C2211yescharacteristic
10C32×C22⋊C8—21no—
11C32×#95C411yescharacteristic, complemented
12C3×#399C2×C314yes—
13C3×#342C2×C314yes—
14C3×#323C2×C314yes—
15C24×C32D411yescharacteristic
16C22×C32×C4—21no—
17C22×C32×C4—21no—
18C22×C32×C4—41no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4D411yescharacteristic
21C2×C32×C8—41no—
22C32×C4⋊C4—42no—
23C32×C4⋊C4—41no—
24C32×C22⋊C4—22no—
25C32×C22⋊C4—41no—
26C32×C22⋊C4—42no—
27C32×C22⋊C4—41no—
28#1352C3211yescharacteristic, direct product factor, Sylow
29C2×C3×C4⋊C4—24no—
30C2×C3×C4⋊C4C3×C414yescomplemented
31C2×C3×C22⋊C4—24no—
32C2×C3×C22⋊C4—24no—
33C2×C3×C22⋊C4C22×C314yes—
34C3×C22⋊C8—24no—
35C3×#95C3×C414yescomplemented
36C23×C32—21no—
37C23×C32—21no—
38C23×C32—41no—
39C23×C32—41no—
40C23×C32C22⋊C411yescharacteristic
41C23×C32SD1611yescharacteristic
42C23×C32Q1611yescharacteristic
43C2×C32×C4—22no—
44C2×C32×C4—21no—
45C2×C32×C4—21no—
46C2×C32×C4—41no—
47C2×C32×C4—41no—
48C2×C32×C4—41no—
49C2×C32×C4—41no—
50C2×C32×C4—42no—
51C2×C32×C4—41no—
52C2×C32×C4—41no—
53C2×C32×C4—41no—
54C2×C32×C4—81no—
55C2×C32×C4—81no—
56C32×C8—81no—
57#399C2×C3211yescharacteristic
58#342C2×C3211yescharacteristic
59#323C2×C3211yescharacteristic
60C24×C3C3×D414yes—
61C22×C3×C4—24no—
62C22×C3×C4—24no—
63C22×C3×C4—44no—
64C22×C3×C4C2×C3×C414yes—
65C22×C3×C4C3×D414yes—
66C2×C3×C8—44no—
67C3×C4⋊C4—44no—
68C3×C4⋊C4—48no—
69C3×C22⋊C4—28no—
70C3×C22⋊C4—44no—
71C3×C22⋊C4—48no—
72C3×C22⋊C4—44no—
73C22×C32—21no—
74C22×C32—21no—
75C22×C32—21no—
76C22×C32—21no—
77C22×C32—41no—
78C22×C32—41no—
79C22×C32—41no—
80C22×C32—41no—
81C22×C32—81no—
82C22×C32#9911yescharacteristic
83C22×C32#10311yescharacteristic
84C22×C32#10411yescharacteristic
85C32×C4—42no—
86C32×C4—41no—
87C32×C4—41no—
88C32×C4—82no—
89C32×C4—81no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4C32×C411yescharacteristic, complemented
92C2×C22⋊C4—21no—
93C2×C22⋊C4—21no—
94C2×C22⋊C4C22×C3211yescharacteristic
95C22⋊C8—21no—
96#95C32×C411yescharacteristic, complemented
97C23×C3—24no—
98C23×C3—24no—
99C23×C3—44no—
100C23×C3—44no—
101C23×C3C3×C22⋊C414yes—
102C23×C3C3×SD1614yes—
103C23×C3C3×Q1614yes—
104C2×C3×C4—28no—
105C2×C3×C4—24no—
106C2×C3×C4—24no—
107C2×C3×C4—44no—
108C2×C3×C4—44no—
109C2×C3×C4—44no—
110C2×C3×C4—44no—
111C2×C3×C4—48no—
112C2×C3×C4—44no—
113C2×C3×C4—44no—
114C2×C3×C4—44no—
115C2×C3×C4—84no—
116C2×C3×C4—84no—
117C3×C8—84no—
118C2×C32—21no—
119C2×C32—21no—
120C2×C32—41no—
121C2×C32—41no—
122C2×C32#32811yescharacteristic
123C2×C32#35211yescharacteristic
124C2×C32#35311yescharacteristic
125C24C32×D411yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—41no—
129C22×C4C2×C32×C411yescharacteristic
130C22×C4C32×D411yescharacteristic
131C2×C8—41no—
132C4⋊C4—41no—
133C4⋊C4—42no—
134C22⋊C4—22no—
135C22⋊C4—41no—
136C22⋊C4—42no—
137C22⋊C4—41no—
138C22×C3—24no—
139C22×C3—24no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3—44no—
143C22×C3—44no—
144C22×C3—44no—
145C22×C3—44no—
146C22×C3—84no—
147C22×C3C3×#9914yes—
148C22×C3C3×#10314yes—
149C22×C3C3×#10414yes—
150C3×C4—48no—
151C3×C4—44no—
152C3×C4—44no—
153C3×C4—88no—
154C3×C4—84no—
155C32#135211yescharacteristic, direct product factor, Sylow
156C23—21no—
157C23—21no—
158C23—41no—
159C23—41no—
160C23C32×C22⋊C411yescharacteristic
161C23C32×SD1611yescharacteristic
162C23C32×Q1611yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—81no—
175C2×C4—81no—
176C8—81no—
177C2×C3—24no—
178C2×C3—24no—
179C2×C3—44no—
180C2×C3—44no—
181C2×C3C3×#32814yes—
182C2×C3C3×#35214yes—
183C2×C3C3×#35314yes—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—41no—
192C22—81no—
193C22C32×#9911yescharacteristic
194C22C32×#10311yescharacteristic
195C22C32×#10411yescharacteristic
196C4—42no—
197C4—41no—
198C4—41no—
199C4—82no—
200C4—81no—
201C3C3×#135214yesdirect product factor
202C2—21no—
203C2—21no—
204C2—41no—
205C2—41no—
206C2C32×#32811yescharacteristic
207C2C32×#35211yescharacteristic
208C2C32×#35311yescharacteristic
subgroupG/H
center, socleC22×C32#99
commutatorC22×C4C2×C32×C4
Frattini, cosocleC2×C22⋊C4C22×C32
prime radicalC24×C32D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C23×C32 ◁ C2×C32×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#1352C3direct (N × H)
6. C2×C32×C4⋊C4C4semidirect
11. C32×#95C4semidirect
28. #1352C32direct (N × H)
30. C2×C3×C4⋊C4C3×C4semidirect
35. C3×#95C3×C4semidirect
91. C2×C4⋊C4C32×C4semidirect
96. #95C32×C4semidirect
155. C32#1352direct (N × H)
201. C3C3×#1352direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#3992
C32×#3422
C32×#3232
C3×#13523