Finite Group Databasebeta

← C2×#19151748 #26029433

Subgroups — C2×#19151748 #26029433

Order 11392.

996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×D356C211yesmaximal, characteristic
2C22×#13083561C212yesmaximal, complemented
3#19151748C218yesmaximal, direct product factor
4C2×#15667932C212yesmaximal, complemented
5C2×C22⋊#10623494C211yesmaximal, characteristic, complemented
6C2×C22⋊Q8×C89C211yesmaximal, characteristic, complemented
7C24×D89—21no—
8C22×D356—28no—
9C22×D356—21no—
10C22×D356—22no—
11C22×D356C2214yes—
12C22×D356C2212yes—
13C2×#13083561—28no—
14C2×#13083561C2218yescomplemented
15C22×#10623494C2212yescomplemented
16#15667932C2218yescomplemented
17C22⋊#10623494C2214yescomplemented
18C22×Q8×C89C2211yescharacteristic, complemented
19C23×C4×C89C2211yescharacteristic
20C22⋊Q8×C89—22no—
21C22⋊Q8×C89C2214yescomplemented
22C2×C4⋊C4×C89—21no—
23C2×C4⋊C4×C89C2211yescharacteristic, complemented
24C2×C22⋊C4×C89—21no—
25C23×D89—28no—
26C23×D89—24no—
27C23×D89—22no—
28C23×D89—44no—
29C23×D89—44no—
30C2×D356—28no—
31C2×D356—216no—
32C2×D356—24no—
33C2×D356—22no—
34C2×D356—24no—
35C2×D356—216no—
36C2×D356D418yes—
37C2×D356C2314yes—
38#13083561—216no—
39C2×#10623494—24no—
40C2×#10623494C2314yescomplemented
41C24×C89D411yescharacteristic
42C2×Q8×C89—21no—
43C2×Q8×C89—24no—
44C2×Q8×C89C2312yescomplemented
45C22×C4×C89—24no—
46C22×C4×C89—21no—
47C22×C4×C89—21no—
48C22×C4×C89D411yescharacteristic
49C22×C4×C89D412yes—
50C22×C4×C89C2312yes—
51C22×C4×C89C2311yescharacteristic
52C4⋊C4×C89—24no—
53C4⋊C4×C89—21no—
54C4⋊C4×C89C2312yescomplemented
55C22⋊C4×C89—24no—
56C23×C89—22no—
57C23×C89—22no—
58C23×C89SD1614yescomplemented
59C23×C89C2×D412yes—
60C23×C89C2×D411yescharacteristic
61C22×D89—216no—
62C22×D89—28no—
63C22×D89—24no—
64C22×D89—48no—
65C22×D89—432no—
66C22×D89—44no—
67C22×D89—48no—
68C22×D89—44no—
69Q8×C89—24no—
70Q8×C89—42no—
71C2×C4×C89—22no—
72C2×C4×C89—24no—
73C2×C4×C89—24no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—42no—
77C2×C4×C89—42no—
78C2×C4×C89C2×D414yes—
79C2×C4×C89C2×D412yes—
80C2×C4×C89C2×D411yescharacteristic
81C2×C4×C89C2411yescharacteristic
82D356—216no—
83D356—28no—
84D356—24no—
85D356C2×D418yes—
86#10623494—24no—
87C22×C89—22no—
88C22×C89—22no—
89C22×C89—28no—
90C22×C89#12012yes—
91C22×C89C2×SD1612yes—
92C22×C89C2×SD1614yescomplemented
93C22×C89AGL(1,ℤ/8)12yes—
94C22×C89C22×D411yescharacteristic
95C2×D89—28no—
96C2×D89—432no—
97C2×D89—44no—
98C2×D89—44no—
99C2×D89—416no—
100C4×C89—22no—
101C4×C89—42no—
102C4×C89—42no—
103C4×C89#12012yes—
104C4×C89C22×D412yes—
105C2×C89—24no—
106C2×C89#45014yescomplemented
107C2×C89C2×#12011yescharacteristic
108C2×C89C22×SD1611yescharacteristic
109C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
110D89—48no—
111C2×#450—891nomaximal, Sylow
112C89C2×#45011yescharacteristic, complemented, Sylow
113C23×D4—891no—
114C22×SD16—892no—
115C2×C22⋊Q8D8911yescharacteristic, complemented
116#450—898no—
117C2×#102—892no—
118C2×C22⋊C8—891no—
119C25—1781no—
120C22×Q8C2×D8911yescharacteristic, complemented
121C22×D4—892no—
122C22×D4—894no—
123C22×D4—1788no—
124C22×D4—1782no—
125C22×D4—1781no—
126C23×C4C2×D8911yescharacteristic
127C2×SD16—898no—
128C2×SD16—1788no—
129C22×C8—892no—
130C22⋊Q8—22no—
131C22⋊Q8C2×D8914yescomplemented
132C2×C4⋊C4—21no—
133C2×C4⋊C4C2×D8911yescharacteristic, complemented
134C2×C22⋊C4—21no—
135#102—898no—
136C22⋊C8—894no—
137C24—3564no—
138C24—3564no—
139C24—1788no—
140C24—1784no—
141C24—1782no—
142C24C22⋊D8911yescharacteristic
143C2×Q8—21no—
144C2×Q8—24no—
145C2×Q8C22×D8912yescomplemented
146C2×D4—898no—
147C2×D4—894no—
148C2×D4—17816no—
149C2×D4—1788no—
150C2×D4—17816no—
151C2×D4—1784no—
152C2×D4—1784no—
153C2×D4—1782no—
154C22×C4—24no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4C22⋊D8912yes—
158C22×C4C22⋊D8911yescharacteristic
159C22×C4C22×D8912yes—
160C22×C4C22×D8911yescharacteristic
161SD16—17816no—
162C2×C8—894no—
163C2×C8—1784no—
164C4⋊C4—24no—
165C4⋊C4—21no—
166C4⋊C4C22×D8912yescomplemented
167C22⋊C4—24no—
168C23—22no—
169C23—22no—
170C23—3568no—
171C23—35632no—
172C23—3564no—
173C23—3568no—
174C23—3564no—
175C23—17816no—
176C23—1788no—
177C23—1784no—
178C23#1308356114yescomplemented
179C23C2×C22⋊D8912yes—
180C23C2×C22⋊D8911yescharacteristic
181Q8—24no—
182Q8—42no—
183D4—898no—
184D4—17816no—
185D4—1788no—
186D4—1784no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4D4×D8914yes—
195C2×C4C2×C22⋊D8912yes—
196C2×C4C2×C22⋊D8911yescharacteristic
197C2×C4C23×D8911yescharacteristic
198C8—1784no—
199C22—22no—
200C22—28no—
201C22—22no—
202C22—35632no—
203C22—3564no—
204C22—35616no—
205C22—3564no—
206C22—1788no—
207C22#1566798012yes—
208C22C2×#1308356112yes—
209C22C2×#1308356114yescomplemented
210C22#1566803712yes—
211C22C22×C22⋊D8911yescharacteristic
212C4—22no—
213C4—42no—
214C4—42no—
215C4#1566798012yes—
216C4C2×D4×D8912yes—
217C2—24no—
218C2—3568no—
219C2#1915174814yesdirect product factor
220C2C2×#1566798011yescharacteristic
221C2C22×#1308356111yescharacteristic
222C2C2×#1566803711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×C22⋊Q8×C89C2
socleC23×C89C2×D4
prime radicalC23×D356C2
hypercenterC2×C22⋊Q8D89
hypocenterC89C2×#450
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#13083561C2semidirect
3. #19151748C2direct (N × H)
4. C2×#15667932C2semidirect
5. C2×C22⋊#10623494C2semidirect
6. C2×C22⋊Q8×C89C2semidirect
14. C2×#13083561C22semidirect
15. C22×#10623494C22semidirect
16. #15667932C22semidirect
17. C22⋊#10623494C22semidirect
18. C22×Q8×C89C22semidirect
21. C22⋊Q8×C89C22semidirect
23. C2×C4⋊C4×C89C22semidirect
40. C2×#10623494C23semidirect
44. C2×Q8×C89C23semidirect
54. C4⋊C4×C89C23semidirect
58. C23×C89SD16semidirect
92. C22×C89C2×SD16semidirect
106. C2×C89#450semidirect
112. C89C2×#450semidirect
115. C2×C22⋊Q8D89semidirect
120. C22×Q8C2×D89semidirect
131. C22⋊Q8C2×D89semidirect
133. C2×C4⋊C4C2×D89semidirect
145. C2×Q8C22×D89semidirect
166. C4⋊C4C22×D89semidirect
178. C23#13083561semidirect
209. C22C2×#13083561semidirect
219. C2#19151748direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3562
C22×#130835612
#191517482
C2×#156679322
C2×C22⋊#106234942
C2×C22⋊Q8×C892
C2×#45089