Finite Group Databasebeta

← #26025621

Subgroups — #26025621

Order 11392.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×#15667977C212yesmaximal
2#19151531C212yesmaximal
3#19151528C211yesmaximal, characteristic
4#19151502C212yesmaximal
5#19151502C212yesmaximal
6#19151495C212yesmaximal
7#19151493C212yesmaximal
8#19151467C211yesmaximal, characteristic
9#398×C89C211yesmaximal, characteristic
10C22×Dic178C2212yes—
11#15667977—28no—
12C2×C4⋊Dic89C2211yescharacteristic
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×C4×Dic89C2212yes—
20C2×C4×Dic89C2212yes—
21C2×C4×Dic89C2211yescharacteristic
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27C2×C4⋊C4×C89C2212yes—
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#95×C89C2212yes—
31#95×C89C2211yescharacteristic
32C2×Dic178—24no—
33C2×Dic178—24no—
34C2×Dic178Q818yescomplemented
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C4⋊Dic89—41no—
40C4⋊Dic89—41no—
41#13083553—24no—
42#13083553—24no—
43#13083553—24no—
44#13083553—24no—
45#13083553—42no—
46C4×Dic89—24no—
47C4×Dic89—24no—
48C4×Dic89D414yes—
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2311yescharacteristic
51C22×C4×C89C2312yes—
52C22×C4×C89C2311yescharacteristic
53C22×C4×C89C2312yes—
54C4⋊C4×C89—24no—
55C4⋊C4×C89—41no—
56C4⋊C4×C89—41no—
57C23×C89C2411yescharacteristic
58C2×C4×C89—22no—
59C2×C4×C89—22no—
60C2×C4×C89—21no—
61C2×C4×C89—21no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89C2×D412yes—
70C2×C4×C89C2×Q814yes—
71C2×Dic89—22no—
72C2×Dic89—22no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89C2×D414yes—
80C2×Dic89C2×Q814yes—
81C2×Dic89C2×Q814yes—
82C2×Dic89#4114yes—
83Dic178—216no—
84C22×C89C22×D411yescharacteristic
85C22×C89C22×Q812yes—
86C22×C89C2×#4112yes—
87C22×C89H(5,𝔽2)11yescharacteristic
88C22×C892−1+411yescharacteristic
89C4×C89—24no—
90C4×C89—22no—
91C4×C89—42no—
92C4×C89—41no—
93C4×C89—41no—
94Dic89—24no—
95Dic89—42no—
96Dic89—42no—
97Dic89C22⋊Q818yes—
98C2×C89C2×C22⋊Q812yes—
99C2×C89#53711yescharacteristic
100C2×C89#55712yes—
101C2×C89Q8211yescharacteristic
102C2×C89#55911yescharacteristic
103#2582—891nomaximal, Sylow
104C89#258211yescharacteristic, complemented, Sylow
105C2×C4×Q8—892no—
106#398—891no—
107#398—892no—
108#398D8911yescharacteristic
109#391—892no—
110#391—892no—
111#389—892no—
112#389—892no—
113#384—891no—
114C22×Q8—892no—
115C4×Q8—1788no—
116C2×C4⋊C4—891no—
117C2×C4⋊C4—892no—
118C2×C4⋊C4—891no—
119C2×C4⋊C4—892no—
120C2×C4⋊C4—892no—
121C2×C4⋊C4—892no—
122C2×C4⋊C4—892no—
123C2×C4⋊C4C2×D8912yes—
124C2×C4⋊C4C2×D8911yescharacteristic
125C2×C4⋊C4C2×D8911yescharacteristic
126C2×C42—891no—
127C2×C42—892no—
128C2×C42—892no—
129#95—892no—
130#95—892no—
131#95—892no—
132#95—891no—
133#95—892no—
134#95C2×D8912yes—
135#95C2×D8911yescharacteristic
136C2×Q8—898no—
137C2×Q8—1784no—
138C2×Q8—1784no—
139C22×C4—892no—
140C22×C4—892no—
141C22×C4—892no—
142C22×C4—892no—
143C22×C4C22×D8911yescharacteristic
144C22×C4C22×D8911yescharacteristic
145C22×C4C22×D8912yes—
146C22×C4C22×D8911yescharacteristic
147C22×C4C22×D8912yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—3562no—
152C4⋊C4—3561no—
153C4⋊C4—3561no—
154C4⋊C4—1784no—
155C4⋊C4—1784no—
156C4⋊C4—1784no—
157C4⋊C4—1784no—
158C42—894no—
159C42—1784no—
160C42—1784no—
161C23C23×D8911yescharacteristic
162Q8—17816no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—894no—
175C2×C4—894no—
176C2×C4—894no—
177C2×C4—894no—
178C2×C4—1782no—
179C2×C4—1782no—
180C2×C4—1782no—
181C2×C4—1782no—
182C2×C4—1782no—
183C2×C4—1782no—
184C2×C4—1782no—
185C2×C4—1782no—
186C2×C4D4×D8912yes—
187C2×C4Q8×D8914yes—
188C22C2×D4×D8911yescharacteristic
189C22C2×Q8×D8912yes—
190C22#41×D8912yes—
191C22#1566805711yescharacteristic
192C22#1566805911yescharacteristic
193C4—22no—
194C4—24no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—898no—
199C4—3562no—
200C4—3562no—
201C4—1784no—
202C2C22⋊Q8×D8912yes—
203C2#1915217511yescharacteristic
204C2#1915232512yes—
205C2#1915232811yescharacteristic
206C2#1915233211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#398×C89C2
hypercenter#398D89
hypocenterC89#2582
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
34. C2×Dic178Q8semidirect
104. C89#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#156679772
#191515312
#191515282
#191515022
#191514952
#191514932
#191514672
#398×C892
#258289