Finite Group Databasebeta

← C32×#2184 #11769233

Subgroups — C32×#2184 #11769233

Order 1152.

798 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 216 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×C32×D8C211yesmaximal, characteristic, complemented
2C2×C32×D16C212yesmaximal, complemented
3C32×#466C211yesmaximal, characteristic, complemented
4C32×#357C212yesmaximal, complemented
5C32×C22⋊C16C211yesmaximal, characteristic, complemented
6C3×#2184C314yesmaximal, direct product factor
7C22×C32×D4—21no—
8C2×C32×D8—24no—
9C2×C32×D8—21no—
10C2×C32×D8C2212yes—
11C2×C32×D8C2211yescharacteristic, complemented
12C22×C32×C8C2211yescharacteristic
13C32×#121—21no—
14C32×D16—24no—
15C2×C32×C16C2212yescomplemented
16C32×#107C2211yescharacteristic, complemented
17C32×#102—21no—
18C22×C3×D8C2×C314yescomplemented
19C2×C3×D16C2×C318yescomplemented
20C3×#466C2×C314yescomplemented
21C3×#357C2×C318yescomplemented
22C3×C22⋊C16C2×C314yescomplemented
23C24×C32—41no—
24C2×C32×D4—24no—
25C2×C32×D4—22no—
26C2×C32×D4—21no—
27C2×C32×D4—42no—
28C2×C32×D4—41no—
29C2×C32×D4—41no—
30C22×C32×C4D411yescharacteristic
31C32×D8—24no—
32C32×D8—22no—
33C32×D8—22no—
34C32×D8D414yescomplemented
35C2×C32×C8—22no—
36C2×C32×C8D411yescharacteristic
37C2×C32×C8C2311yescharacteristic
38C32×C4⋊C4—21no—
39C32×C22⋊C4—41no—
40C32×C16—22no—
41#2184C3211yescharacteristic, direct product factor, Sylow
42C22×C3×D4—24no—
43C2×C3×D8—216no—
44C2×C3×D8—24no—
45C2×C3×D8C22×C318yes—
46C2×C3×D8C22×C314yescomplemented
47C22×C3×C8C22×C314yes—
48C3×#121—24no—
49C3×D16—216no—
50C2×C3×C16C22×C318yescomplemented
51C3×#107C22×C314yescomplemented
52C3×#102—24no—
53C23×C32—44no—
54C23×C32—42no—
55C23×C32—41no—
56C23×C32—82no—
57C23×C32—82no—
58C23×C32D811yescharacteristic
59C32×D4—24no—
60C32×D4—44no—
61C32×D4—41no—
62C32×D4—42no—
63C32×D4—41no—
64C32×D4—82no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4—41no—
68C2×C32×C4D811yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C32×C8—21no—
71C32×C8C2×D412yes—
72C22×D8C2×C3211yescharacteristic, complemented
73C2×D16C2×C3212yescomplemented
74#466C2×C3211yescharacteristic, complemented
75#357C2×C3212yescomplemented
76C22⋊C16C2×C3211yescharacteristic, complemented
77C24×C3—44no—
78C2×C3×D4—216no—
79C2×C3×D4—28no—
80C2×C3×D4—24no—
81C2×C3×D4—48no—
82C2×C3×D4—44no—
83C2×C3×D4—44no—
84C22×C3×C4C3×D414yes—
85C3×D8—216no—
86C3×D8—28no—
87C3×D8—28no—
88C3×D8C3×D4116yescomplemented
89C2×C3×C8—28no—
90C2×C3×C8C3×D414yes—
91C2×C3×C8C23×C314yes—
92C3×C4⋊C4—24no—
93C3×C22⋊C4—44no—
94C3×C16—28no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—44no—
98C22×C32—88no—
99C22×C32—82no—
100C22×C32—82no—
101C22×C32—81no—
102C22×C32—81no—
103C22×C32—81no—
104C22×C32D1612yescomplemented
105C22×C32C2×D811yescharacteristic
106C32×C4—21no—
107C32×C4—81no—
108C32×C4#12011yescharacteristic
109C32×C4AGL(1,ℤ/8)11yescharacteristic
110C22×D4—21no—
111C2×D8—24no—
112C2×D8—21no—
113C2×D8C22×C3212yes—
114C2×D8C22×C3211yescharacteristic, complemented
115C22×C8C22×C3211yescharacteristic
116#121—21no—
117D16—24no—
118C2×C16C22×C3212yescomplemented
119#107C22×C3211yescharacteristic, complemented
120#102—21no—
121C23×C3—416no—
122C23×C3—48no—
123C23×C3—44no—
124C23×C3—88no—
125C23×C3—88no—
126C23×C3C3×D814yes—
127C3×D4—216no—
128C3×D4—416no—
129C3×D4—44no—
130C3×D4—48no—
131C3×D4—44no—
132C3×D4—88no—
133C2×C3×C4—24no—
134C2×C3×C4—24no—
135C2×C3×C4—44no—
136C2×C3×C4C3×D814yes—
137C2×C3×C4C2×C3×D414yes—
138C3×C8—24no—
139C3×C8C2×C3×D418yes—
140C2×C32—22no—
141C2×C32—84no—
142C2×C32—161no—
143C2×C32#44711yescharacteristic
144C2×C32C2×D1611yescharacteristic
145C2×C32#50911yescharacteristic
146C24—41no—
147C2×D4—24no—
148C2×D4—22no—
149C2×D4—21no—
150C2×D4—42no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4C32×D411yescharacteristic
154D8—24no—
155D8—22no—
156D8—22no—
157D8C32×D414yescomplemented
158C2×C8—22no—
159C2×C8C32×D411yescharacteristic
160C2×C8C23×C3211yescharacteristic
161C4⋊C4—21no—
162C22⋊C4—41no—
163C16—22no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3—416no—
167C22×C3—832no—
168C22×C3—88no—
169C22×C3—88no—
170C22×C3—84no—
171C22×C3—84no—
172C22×C3—84no—
173C22×C3C3×D1618yescomplemented
174C22×C3C2×C3×D814yes—
175C3×C4—24no—
176C3×C4—84no—
177C3×C4C3×#12014yes—
178C3×C4C3×AGL(1,ℤ/8)14yes—
179C32#218411yescharacteristic, direct product factor, Sylow
180C23—44no—
181C23—42no—
182C23—41no—
183C23—82no—
184C23—82no—
185C23C32×D811yescharacteristic
186D4—24no—
187D4—44no—
188D4—41no—
189D4—42no—
190D4—41no—
191D4—82no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4C32×D811yescharacteristic
196C2×C4C2×C32×D411yescharacteristic
197C8—21no—
198C8C2×C32×D412yes—
199C2×C3—28no—
200C2×C3—816no—
201C2×C3—164no—
202C2×C3C3×#44714yes—
203C2×C3C2×C3×D1614yes—
204C2×C3C3×#50914yes—
205C22—21no—
206C22—21no—
207C22—44no—
208C22—88no—
209C22—82no—
210C22—82no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22C32×D1612yescomplemented
215C22C2×C32×D811yescharacteristic
216C4—21no—
217C4—81no—
218C4C32×#12011yescharacteristic
219C4C32×AGL(1,ℤ/8)11yescharacteristic
220C3C3×#218414yesdirect product factor
221C2—22no—
222C2—84no—
223C2—161no—
224C2C32×#44711yescharacteristic
225C2C2×C32×D1611yescharacteristic
226C2C32×#50911yescharacteristic
subgroupG/H
center, socleC22×C32C2×D8
commutator, Frattini, cosocleC2×C8C23×C32
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C22×C32×C4 ◁ C22×C32×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C32×D8C2semidirect
2. C2×C32×D16C2semidirect
3. C32×#466C2semidirect
4. C32×#357C2semidirect
5. C32×C22⋊C16C2semidirect
6. C3×#2184C3direct (N × H)
11. C2×C32×D8C22semidirect
15. C2×C32×C16C22semidirect
16. C32×#107C22semidirect
18. C22×C3×D8C2×C3semidirect
19. C2×C3×D16C2×C3semidirect
20. C3×#466C2×C3semidirect
21. C3×#357C2×C3semidirect
22. C3×C22⋊C16C2×C3semidirect
34. C32×D8D4semidirect
41. #2184C32direct (N × H)
46. C2×C3×D8C22×C3semidirect
50. C2×C3×C16C22×C3semidirect
51. C3×#107C22×C3semidirect
72. C22×D8C2×C32semidirect
73. C2×D16C2×C32semidirect
74. #466C2×C32semidirect
75. #357C2×C32semidirect
76. C22⋊C16C2×C32semidirect
88. C3×D8C3×D4semidirect
104. C22×C32D16semidirect
114. C2×D8C22×C32semidirect
118. C2×C16C22×C32semidirect
119. #107C22×C32semidirect
157. D8C32×D4semidirect
173. C22×C3C3×D16semidirect
179. C32#2184direct (N × H)
214. C22C32×D16semidirect
220. C3C3×#2184direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×D82
C2×C32×D162
C32×#4662
C32×#3572
C32×C22⋊C162
C3×#21843