Finite Group Databasebeta

← C32×#2190 #11769239

Subgroups — C32×#2190 #11769239

Order 1152.

678 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 192 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×#575C211yesmaximal, characteristic, complemented
2C32×#509C212yesmaximal, complemented
3C32×#469C211yesmaximal, characteristic, complemented
4C32×#360C212yesmaximal, complemented
5C32×#349C211yesmaximal, characteristic, complemented
6C3×#2190C314yesmaximal, direct product factor
7C2×C32×#41—21no—
8C32×#137—22no—
9C32×AGL(1,ℤ/8)—22no—
10C32×#135—21no—
11C32×#135C2212yes—
12C2×C32×D8C2211yescharacteristic, complemented
13C2×C32×M16C2211yescharacteristic
14C32×#121—21no—
15C32×SD32—22no—
16C32×D16—22no—
17C32×M32C2212yescomplemented
18C32×#106C2211yescharacteristic, complemented
19C32×#102—21no—
20C3×#575C2×C314yescomplemented
21C3×#509C2×C318yescomplemented
22C3×#469C2×C314yescomplemented
23C3×#360C2×C318yescomplemented
24C3×#349C2×C314yescomplemented
25C32×#41—22no—
26C32×#41—22no—
27C32×#41—41no—
28C32×#41—41no—
29C2×C32×Q8—21no—
30C2×C32×D4—21no—
31C2×C32×D4—21no—
32C2×C32×D4—41no—
33C2×C32×D4—41no—
34C22×C32×C4—41no—
35C22×C32×C4D411yescharacteristic
36C32×Q16—21no—
37C32×Q16D412yescomplemented
38C32×SD16—22no—
39C32×SD16—22no—
40C32×D8—21no—
41C32×D8—22no—
42C32×D8D412yescomplemented
43C32×M16—22no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46C32×C4⋊C4—21no—
47C32×C22⋊C4—41no—
48C32×C16—22no—
49#2190C3211yescharacteristic, direct product factor, Sylow
50C2×C3×#41—24no—
51C3×#137—28no—
52C3×AGL(1,ℤ/8)—28no—
53C3×#135—24no—
54C3×#135C22×C318yes—
55C2×C3×D8C22×C314yescomplemented
56C2×C3×M16C22×C314yes—
57C3×#121—24no—
58C3×SD32—28no—
59C3×D16—28no—
60C3×M32C22×C318yescomplemented
61C3×#106C22×C314yescomplemented
62C3×#102—24no—
63C23×C32—41no—
64C23×C32—41no—
65C23×C32D811yescharacteristic
66C32×Q8—22no—
67C32×Q8—41no—
68C32×D4—22no—
69C32×D4—41no—
70C32×D4—42no—
71C32×D4—42no—
72C32×D4—41no—
73C32×D4—41no—
74C32×D4—82no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—42no—
78C2×C32×C4—41no—
79C2×C32×C4—42no—
80C2×C32×C4—41no—
81C2×C32×C4D811yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C32×C8—21no—
84C32×C8C2×D412yes—
85#575C2×C3211yescharacteristic, complemented
86#509C2×C3212yescomplemented
87#469C2×C3211yescharacteristic, complemented
88#360C2×C3212yescomplemented
89#349C2×C3211yescharacteristic, complemented
90C3×#41—28no—
91C3×#41—28no—
92C3×#41—44no—
93C3×#41—44no—
94C2×C3×Q8—24no—
95C2×C3×D4—24no—
96C2×C3×D4—24no—
97C2×C3×D4—44no—
98C2×C3×D4—44no—
99C22×C3×C4—44no—
100C22×C3×C4C3×D414yes—
101C3×Q16—24no—
102C3×Q16C3×D418yescomplemented
103C3×SD16—28no—
104C3×SD16—28no—
105C3×D8—24no—
106C3×D8—28no—
107C3×D8C3×D418yescomplemented
108C3×M16—28no—
109C2×C3×C8C3×D414yes—
110C2×C3×C8C23×C314yes—
111C3×C4⋊C4—24no—
112C3×C22⋊C4—44no—
113C3×C16—28no—
114C22×C32—21no—
115C22×C32—41no—
116C22×C32—42no—
117C22×C32—81no—
118C22×C32—81no—
119C22×C32—82no—
120C22×C32—81no—
121C22×C32C2×D811yescharacteristic
122C32×C4—21no—
123C32×C4—42no—
124C32×C4—81no—
125C32×C4#12011yescharacteristic
126C32×C4AGL(1,ℤ/8)11yescharacteristic
127C2×#41—21no—
128#137—22no—
129AGL(1,ℤ/8)—22no—
130#135—21no—
131#135C22×C3212yes—
132C2×D8C22×C3211yescharacteristic, complemented
133C2×M16C22×C3211yescharacteristic
134#121—21no—
135SD32—22no—
136D16—22no—
137M32C22×C3212yescomplemented
138#106C22×C3211yescharacteristic, complemented
139#102—21no—
140C23×C3—44no—
141C23×C3—44no—
142C23×C3C3×D814yes—
143C3×Q8—28no—
144C3×Q8—44no—
145C3×D4—28no—
146C3×D4—44no—
147C3×D4—48no—
148C3×D4—48no—
149C3×D4—44no—
150C3×D4—44no—
151C3×D4—88no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—48no—
155C2×C3×C4—44no—
156C2×C3×C4—48no—
157C2×C3×C4—44no—
158C2×C3×C4C3×D814yes—
159C2×C3×C4C2×C3×D414yes—
160C3×C8—24no—
161C3×C8C2×C3×D418yes—
162C2×C32—21no—
163C2×C32—41no—
164C2×C32—82no—
165C2×C32—161no—
166C2×C32#44711yescharacteristic
167#41—22no—
168#41—22no—
169#41—41no—
170#41—41no—
171C2×Q8—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—41no—
175C2×D4—41no—
176C22×C4—41no—
177C22×C4C32×D411yescharacteristic
178Q16—21no—
179Q16C32×D412yescomplemented
180SD16—22no—
181SD16—22no—
182D8—21no—
183D8—22no—
184D8C32×D412yescomplemented
185M16—22no—
186C2×C8C32×D411yescharacteristic
187C2×C8C23×C3211yescharacteristic
188C4⋊C4—21no—
189C22⋊C4—41no—
190C16—22no—
191C22×C3—24no—
192C22×C3—44no—
193C22×C3—48no—
194C22×C3—84no—
195C22×C3—84no—
196C22×C3—88no—
197C22×C3—84no—
198C22×C3C2×C3×D814yes—
199C3×C4—24no—
200C3×C4—48no—
201C3×C4—84no—
202C3×C4C3×#12014yes—
203C3×C4C3×AGL(1,ℤ/8)14yes—
204C32#219011yescharacteristic, direct product factor, Sylow
205C23—41no—
206C23—41no—
207C23C32×D811yescharacteristic
208Q8—22no—
209Q8—41no—
210D4—22no—
211D4—41no—
212D4—42no—
213D4—42no—
214D4—41no—
215D4—41no—
216D4—82no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4C32×D811yescharacteristic
224C2×C4C2×C32×D411yescharacteristic
225C8—21no—
226C8C2×C32×D412yes—
227C2×C3—24no—
228C2×C3—44no—
229C2×C3—88no—
230C2×C3—164no—
231C2×C3C3×#44714yes—
232C22—21no—
233C22—41no—
234C22—42no—
235C22—81no—
236C22—81no—
237C22—82no—
238C22—81no—
239C22C2×C32×D811yescharacteristic
240C4—21no—
241C4—42no—
242C4—81no—
243C4C32×#12011yescharacteristic
244C4C32×AGL(1,ℤ/8)11yescharacteristic
245C3C3×#219014yesdirect product factor
246C2—21no—
247C2—41no—
248C2—82no—
249C2—161no—
250C2C32×#44711yescharacteristic
subgroupG/H
center, socleC2×C32#447
commutator, Frattini, cosocleC2×C8C23×C32
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C2×C32×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C32×#575C2semidirect
2. C32×#509C2semidirect
3. C32×#469C2semidirect
4. C32×#360C2semidirect
5. C32×#349C2semidirect
6. C3×#2190C3direct (N × H)
12. C2×C32×D8C22semidirect
17. C32×M32C22semidirect
18. C32×#106C22semidirect
20. C3×#575C2×C3semidirect
21. C3×#509C2×C3semidirect
22. C3×#469C2×C3semidirect
23. C3×#360C2×C3semidirect
24. C3×#349C2×C3semidirect
37. C32×Q16D4semidirect
42. C32×D8D4semidirect
49. #2190C32direct (N × H)
55. C2×C3×D8C22×C3semidirect
60. C3×M32C22×C3semidirect
61. C3×#106C22×C3semidirect
85. #575C2×C32semidirect
86. #509C2×C32semidirect
87. #469C2×C32semidirect
88. #360C2×C32semidirect
89. #349C2×C32semidirect
102. C3×Q16C3×D4semidirect
107. C3×D8C3×D4semidirect
132. C2×D8C22×C32semidirect
137. M32C22×C32semidirect
138. #106C22×C32semidirect
179. Q16C32×D4semidirect
184. D8C32×D4semidirect
204. C32#2190direct (N × H)
245. C3C3×#2190direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#5752
C32×#5092
C32×#4692
C32×#3602
C32×#3492
C3×#21903