Finite Group Databasebeta

← C32×#1343 #11768392

Subgroups — C32×#1343 #11768392

Order 1152.

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

normal subgroups only

This group has 666 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×#392C211yesmaximal, characteristic
2C32×#342C211yesmaximal, characteristic, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4C3×#1343C314yesmaximal, direct product factor
5C22×C32×D4—21no—
6C22×C32×D4C411yescharacteristic, complemented
7C2×C32×C22⋊C4—21no—
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4C2211yescharacteristic
10C32×C22⋊C8—21no—
11C32×#95C411yescharacteristic, complemented
12C3×#392C2×C314yes—
13C3×#342C2×C314yescomplemented
14C3×#323C2×C314yescomplemented
15C24×C32—21no—
16C24×C32D411yescharacteristic
17C2×C32×D4—42no—
18C2×C32×D4—41no—
19C2×C32×D4—42no—
20C2×C32×D4—41no—
21C2×C32×D4—41no—
22C2×C32×D4—42no—
23C22×C32×C4—21no—
24C22×C32×C4—41no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C2×C32×C8—41no—
28C32×C22⋊C4—22no—
29C32×C22⋊C4—41no—
30C32×C22⋊C4—42no—
31C32×C22⋊C4—41no—
32#1343C3211yescharacteristic, direct product factor, Sylow
33C22×C3×D4—24no—
34C22×C3×D4C3×C414yescomplemented
35C2×C3×C22⋊C4—24no—
36C2×C3×C22⋊C4—24no—
37C2×C3×C22⋊C4C22×C314yes—
38C3×C22⋊C8—24no—
39C3×#95C3×C414yescomplemented
40C23×C32—21no—
41C23×C32—21no—
42C23×C32—22no—
43C23×C32—41no—
44C23×C32—41no—
45C23×C32—41no—
46C23×C32—41no—
47C23×C32—41no—
48C23×C32—41no—
49C23×C32—41no—
50C23×C32—41no—
51C23×C32C22⋊C411yescharacteristic
52C23×C32D811yescharacteristic
53C23×C32SD1611yescharacteristic
54C32×D4—42no—
55C32×D4—44no—
56C32×D4—44no—
57C32×D4—42no—
58C2×C32×C4—22no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—42no—
66C2×C32×C4—81no—
67C2×C32×C4—81no—
68C32×C8—81no—
69#392C2×C3211yescharacteristic
70#342C2×C3211yescharacteristic, complemented
71#323C2×C3211yescharacteristic, complemented
72C24×C3—24no—
73C24×C3C3×D414yes—
74C2×C3×D4—44no—
75C2×C3×D4—48no—
76C2×C3×D4—48no—
77C2×C3×D4—44no—
78C2×C3×D4—44no—
79C2×C3×D4—48no—
80C22×C3×C4—24no—
81C22×C3×C4—44no—
82C22×C3×C4C2×C3×C414yes—
83C22×C3×C4C3×D414yes—
84C2×C3×C8—44no—
85C3×C22⋊C4—28no—
86C3×C22⋊C4—44no—
87C3×C22⋊C4—48no—
88C3×C22⋊C4—44no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32—41no—
94C22×C32—41no—
95C22×C32—42no—
96C22×C32—42no—
97C22×C32—41no—
98C22×C32—41no—
99C22×C32—42no—
100C22×C32—81no—
101C22×C32—81no—
102C22×C32—81no—
103C22×C32—81no—
104C22×C32—81no—
105C22×C32#9911yescharacteristic
106C22×C32#10211yescharacteristic
107C22×C32#10411yescharacteristic
108C32×C4—42no—
109C32×C4—41no—
110C32×C4—41no—
111C32×C4—82no—
112C22×D4—21no—
113C22×D4C32×C411yescharacteristic, complemented
114C2×C22⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C22⋊C4C22×C3211yescharacteristic
117C22⋊C8—21no—
118#95C32×C411yescharacteristic, complemented
119C23×C3—24no—
120C23×C3—24no—
121C23×C3—28no—
122C23×C3—44no—
123C23×C3—44no—
124C23×C3—44no—
125C23×C3—44no—
126C23×C3—44no—
127C23×C3—44no—
128C23×C3—44no—
129C23×C3—44no—
130C23×C3C3×C22⋊C414yes—
131C23×C3C3×D814yes—
132C23×C3C3×SD1614yes—
133C3×D4—48no—
134C3×D4—416no—
135C3×D4—416no—
136C3×D4—48no—
137C2×C3×C4—28no—
138C2×C3×C4—24no—
139C2×C3×C4—24no—
140C2×C3×C4—44no—
141C2×C3×C4—44no—
142C2×C3×C4—44no—
143C2×C3×C4—44no—
144C2×C3×C4—48no—
145C2×C3×C4—84no—
146C2×C3×C4—84no—
147C3×C8—84no—
148C2×C32—21no—
149C2×C32—21no—
150C2×C32—41no—
151C2×C32—41no—
152C2×C32—82no—
153C2×C32#32711yescharacteristic
154C2×C32AΣL(1,𝔽16)11yescharacteristic
155C2×C32#35311yescharacteristic
156C24—21no—
157C24C32×D411yescharacteristic
158C2×D4—41no—
159C2×D4—42no—
160C2×D4—42no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—42no—
164C22×C4—21no—
165C22×C4—41no—
166C22×C4C2×C32×C411yescharacteristic
167C22×C4C32×D411yescharacteristic
168C2×C8—41no—
169C22⋊C4—22no—
170C22⋊C4—41no—
171C22⋊C4—42no—
172C22⋊C4—41no—
173C22×C3—24no—
174C22×C3—24no—
175C22×C3—24no—
176C22×C3—24no—
177C22×C3—44no—
178C22×C3—44no—
179C22×C3—48no—
180C22×C3—48no—
181C22×C3—44no—
182C22×C3—44no—
183C22×C3—48no—
184C22×C3—84no—
185C22×C3—84no—
186C22×C3—84no—
187C22×C3—84no—
188C22×C3—84no—
189C22×C3C3×#9914yes—
190C22×C3C3×#10214yes—
191C22×C3C3×#10414yes—
192C3×C4—48no—
193C3×C4—44no—
194C3×C4—44no—
195C3×C4—88no—
196C32#134311yescharacteristic, direct product factor, Sylow
197C23—21no—
198C23—21no—
199C23—22no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—41no—
205C23—41no—
206C23—41no—
207C23—41no—
208C23C32×C22⋊C411yescharacteristic
209C23C32×D811yescharacteristic
210C23C32×SD1611yescharacteristic
211D4—42no—
212D4—44no—
213D4—44no—
214D4—42no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—81no—
225C8—81no—
226C2×C3—24no—
227C2×C3—24no—
228C2×C3—44no—
229C2×C3—44no—
230C2×C3—88no—
231C2×C3C3×#32714yes—
232C2×C3C3×AΣL(1,𝔽16)14yes—
233C2×C3C3×#35314yes—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—42no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—81no—
249C22—81no—
250C22C32×#9911yescharacteristic
251C22C32×#10211yescharacteristic
252C22C32×#10411yescharacteristic
253C4—42no—
254C4—41no—
255C4—41no—
256C4—82no—
257C3C3×#134314yesdirect product factor
258C2—21no—
259C2—21no—
260C2—41no—
261C2—41no—
262C2—82no—
263C2C32×#32711yescharacteristic
264C2C32×AΣL(1,𝔽16)11yescharacteristic
265C2C32×#35311yescharacteristic
subgroupG/H
center, socleC22×C32#99
commutatorC22×C4C2×C32×C4
Frattini, cosocleC2×C22⋊C4C22×C32
prime radicalC32×#392C2
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
2. C32×#342C2semidirect
3. C32×#323C2semidirect
4. C3×#1343C3direct (N × H)
6. C22×C32×D4C4semidirect
11. C32×#95C4semidirect
13. C3×#342C2×C3semidirect
14. C3×#323C2×C3semidirect
32. #1343C32direct (N × H)
34. C22×C3×D4C3×C4semidirect
39. C3×#95C3×C4semidirect
70. #342C2×C32semidirect
71. #323C2×C32semidirect
113. C22×D4C32×C4semidirect
118. #95C32×C4semidirect
196. C32#1343direct (N × H)
257. C3C3×#1343direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#3922
C32×#3422
C32×#3232
C3×#13433