Finite Group Databasebeta

← #26026199

Subgroups — #26026199

Order 11392.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15668011C211yesmaximal, characteristic
2C2×#15668002C211yesmaximal, characteristic
3#19151540C212yesmaximal
4#19151539C212yesmaximal
5#19151538C211yesmaximal, characteristic
6#19151537C211yesmaximal, characteristic
7#19151536C211yesmaximal, characteristic
8#19151502C212yesmaximal
9#19151502C212yesmaximal
10#19151443C211yesmaximal, characteristic
11#400×C89C211yesmaximal, characteristic
12C22×Dic178C2212yes—
13#15668011—24no—
14#15668002—24no—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×C4×Dic89C2212yes—
23C2×C4×Dic89C2211yescharacteristic
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C2×Dic178—24no—
38C2×Dic178—28no—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C4⋊Dic89—22no—
46C4⋊Dic89—22no—
47#13083553—22no—
48#13083553—22no—
49#13083553—22no—
50#13083553—22no—
51#13083553—24no—
52C4×Dic89—24no—
53C4×Dic89D414yes—
54C22×C4×C89C2312yes—
55C22×C4×C89C2312yes—
56C22×C4×C89C2311yescharacteristic
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C4⋊C4×C89—22no—
60C4⋊C4×C89—22no—
61C23×C89C2411yescharacteristic
62C2×C4×C89—22no—
63C2×C4×C89—21no—
64C2×C4×C89—21no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—24no—
68C2×C4×C89—21no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89C2×D412yes—
74C2×Dic89—21no—
75C2×Dic89—21no—
76C2×Dic89—21no—
77C2×Dic89—21no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—24no—
81C2×Dic89—22no—
82C2×Dic89—21no—
83C2×Dic89—22no—
84C2×Dic89—21no—
85C2×Dic89—22no—
86C2×Dic89C2×D412yes—
87C2×Dic89C2×D412yes—
88C2×Dic89#4114yes—
89Dic178—48no—
90C22×C89C22×D411yescharacteristic
91C22×C89C2×#4112yes—
92C22×C892−1+412yes—
93C22×C892−1+411yescharacteristic
94C22×C892−1+411yescharacteristic
95C4×C89—22no—
96C4×C89—42no—
97C4×C89—41no—
98C4×C89—41no—
99C4×C89—42no—
100Dic89—22no—
101Dic89—42no—
102Dic89—41no—
103Dic89—41no—
104Dic89—42no—
105Dic89#12414yes—
106C2×C89C2×#12411yescharacteristic
107C2×C89#53611yescharacteristic
108C2×C89#53611yescharacteristic
109C2×C89#54112yes—
110C2×C89#54112yes—
111#2642—891nomaximal, Sylow
112C89#264211yescharacteristic, complemented, Sylow
113C2×C4⋊Q8—891no—
114C2×#125—891no—
115#400—891no—
116#400—891no—
117#400—891no—
118#400—892no—
119#400—892no—
120#400D8911yescharacteristic
121#391—892no—
122#391—892no—
123#376—891no—
124C22×Q8—892no—
125C4⋊Q8—1784no—
126#125—1784no—
127C2×C4⋊C4—891no—
128C2×C4⋊C4—891no—
129C2×C4⋊C4—891no—
130C2×C4⋊C4—891no—
131C2×C4⋊C4—891no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—891no—
134C2×C4⋊C4C2×D8911yescharacteristic
135C2×C4⋊C4C2×D8911yescharacteristic
136C2×C42—891no—
137C2×C42—892no—
138#95—892no—
139#95—891no—
140#95—892no—
141#95—892no—
142#95—892no—
143#95—892no—
144#95—892no—
145#95—892no—
146#95C2×D8911yescharacteristic
147#95C2×D8912yes—
148#95C2×D8912yes—
149C2×Q8—1784no—
150C2×Q8—1788no—
151C22×C4—891no—
152C22×C4—891no—
153C22×C4—892no—
154C22×C4—891no—
155C22×C4—891no—
156C22×C4—892no—
157C22×C4C22×D8912yes—
158C22×C4C22×D8911yescharacteristic
159C22×C4C22×D8911yescharacteristic
160C22×C4C22×D8912yes—
161C22×C4C22×D8911yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1782no—
165C4⋊C4—1782no—
166C4⋊C4—1782no—
167C4⋊C4—1782no—
168C4⋊C4—1784no—
169C4⋊C4—1782no—
170C4⋊C4—1782no—
171C42—894no—
172C42—1784no—
173C23C23×D8911yescharacteristic
174Q8—3568no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—892no—
187C2×C4—894no—
188C2×C4—892no—
189C2×C4—1781no—
190C2×C4—1781no—
191C2×C4—1782no—
192C2×C4—1782no—
193C2×C4—1784no—
194C2×C4—1782no—
195C2×C4—1781no—
196C2×C4—1782no—
197C2×C4—1781no—
198C2×C4—1782no—
199C2×C4—1781no—
200C2×C4—1781no—
201C2×C4D4×D8912yes—
202C22C2×D4×D8911yescharacteristic
203C22#41×D8912yes—
204C22#1566805912yes—
205C22#1566805911yescharacteristic
206C22#1566806011yescharacteristic
207C4—22no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—42no—
212C4—894no—
213C4—3561no—
214C4—3561no—
215C4—3562no—
216C4—3562no—
217C4—1782no—
218C2#124×D8911yescharacteristic
219C2#1915217011yescharacteristic
220C2#1915217111yescharacteristic
221C2#1915220512yes—
222C2#1915220712yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#400×C89C2
hypercenter#400D89
hypocenterC89#2642
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
112. C89#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156680022
#191515402
#191515392
#191515382
#191515372
#191515362
#191515022
#191514432
#400×C892
#264289