Finite Group Databasebeta

← #26027202

Subgroups — #26027202

Order 11392.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668002C212yesmaximal
2#19151532C212yesmaximal
3#19151531C212yesmaximal
4#19151529C212yesmaximal
5#19151496C211yesmaximal, characteristic
6#19151496C211yesmaximal, characteristic
7#19151493C212yesmaximal
8#19151481C212yesmaximal
9#389×C89C211yesmaximal, characteristic
10#15668002—28no—
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2211yescharacteristic
13C2×C4⋊Dic89C2211yescharacteristic
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×C4×Dic89C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2212yes—
29C2×C4⋊C4×C89C2211yescharacteristic
30C2×C42×C89C2211yescharacteristic
31#95×C89C2212yes—
32C22×Dic89C2312yes—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C4⋊Dic89—41no—
37C4⋊Dic89—41no—
38C4⋊Dic89D414yes—
39C4⋊Dic89Q814yes—
40#13083553—24no—
41#13083553—24no—
42#13083553—24no—
43#13083553—24no—
44#13083553—24no—
45#13083553—42no—
46C4×Dic89—24no—
47C22×C4×C89C2312yes—
48C22×C4×C89C2312yes—
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2311yescharacteristic
51C22×C4×C89C2311yescharacteristic
52C4⋊C4×C89—24no—
53C4⋊C4×C89—22no—
54C4⋊C4×C89—41no—
55C42×C89—41no—
56C23×C89C2411yescharacteristic
57C2×C4×C89—21no—
58C2×C4×C89—21no—
59C2×C4×C89—21no—
60C2×C4×C89—21no—
61C2×C4×C89—21no—
62C2×C4×C89—21no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89C2×D412yes—
70C2×C4×C89C2×Q812yes—
71C2×C4×C89#4112yes—
72C2×Dic89—22no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89C2×D414yes—
83C2×Dic89C2×Q814yes—
84C22×C89C22×D411yescharacteristic
85C22×C89C22×Q811yescharacteristic
86C22×C89C2×#4111yescharacteristic
87C22×C89H(5,𝔽2)11yescharacteristic
88C22×C892−1+411yescharacteristic
89C22×C892−1+411yescharacteristic
90C22×C892−1+411yescharacteristic
91C4×C89—22no—
92C4×C89—22no—
93C4×C89—22no—
94C4×C89—42no—
95C4×C89—42no—
96Dic89—24no—
97Dic89—24no—
98Dic89—42no—
99Dic89—42no—
100C2×C89#53711yescharacteristic
101C2×C89#53911yescharacteristic
102C2×C89#54411yescharacteristic
103C2×C89#54711yescharacteristic
104C2×C89D4×Q811yescharacteristic
105C2×C89#55711yescharacteristic
106C2×C89#56411yescharacteristic
107#2726—891nomaximal, Sylow
108C89#272611yescharacteristic, complemented, Sylow
109C2×#125—892no—
110#398—892no—
111#398—892no—
112#398—892no—
113#389—892no—
114#389—891no—
115#389—891no—
116#389D8911yescharacteristic
117#387—892no—
118#125—1788no—
119C2×C4⋊C4—891no—
120C2×C4⋊C4—891no—
121C2×C4⋊C4—892no—
122C2×C4⋊C4—891no—
123C2×C4⋊C4—891no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—892no—
129C2×C4⋊C4C2×D8912yes—
130C2×C4⋊C4C2×D8911yescharacteristic
131C2×C4⋊C4C2×D8911yescharacteristic
132C2×C42—892no—
133C2×C42C2×D8911yescharacteristic
134#95—892no—
135#95—892no—
136#95—892no—
137#95—892no—
138#95—892no—
139#95C2×D8912yes—
140C22×C4—892no—
141C22×C4—892no—
142C22×C4—892no—
143C22×C4—892no—
144C22×C4C22×D8912yes—
145C22×C4C22×D8912yes—
146C22×C4C22×D8911yescharacteristic
147C22×C4C22×D8911yescharacteristic
148C22×C4C22×D8911yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—22no—
151C4⋊C4—41no—
152C4⋊C4—894no—
153C4⋊C4—894no—
154C4⋊C4—3562no—
155C4⋊C4—3561no—
156C4⋊C4—3561no—
157C4⋊C4—1784no—
158C4⋊C4—1784no—
159C4⋊C4—1784no—
160C4⋊C4—1784no—
161C4⋊C4—1784no—
162C42—41no—
163C42—1784no—
164C23C23×D8911yescharacteristic
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—894no—
178C2×C4—894no—
179C2×C4—1782no—
180C2×C4—1782no—
181C2×C4—1782no—
182C2×C4—1782no—
183C2×C4—1782no—
184C2×C4—1782no—
185C2×C4—1782no—
186C2×C4—1782no—
187C2×C4—1782no—
188C2×C4—1782no—
189C2×C4D4×D8912yes—
190C2×C4Q8×D8912yes—
191C2×C4#1308357412yes—
192C22C2×D4×D8911yescharacteristic
193C22C2×Q8×D8911yescharacteristic
194C22C2×#1308357411yescharacteristic
195C22#1566805711yescharacteristic
196C22#1566805911yescharacteristic
197C22#1566805911yescharacteristic
198C22#1566806011yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—42no—
204C4—3562no—
205C4—3562no—
206C4—1784no—
207C4—1784no—
208C2#1915217511yescharacteristic
209C2#1915219511yescharacteristic
210C2#1915222711yescharacteristic
211C2#1915225311yescharacteristic
212C2#1915226311yescharacteristic
213C2#1915232611yescharacteristic
214C2C89⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#389×C89C2
hypercenter#389D89
hypocenterC89#2726
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
108. C89#2726semidirect

Maximal subgroups

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

subgroupindex
C2×#156680022
#191515322
#191515312
#191515292
#191514962
#191514932
#191514812
#389×C892
#272689