Finite Group Databasebeta

← #26026375

Subgroups — #26026375

Order 11392.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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#19151530C211yesmaximal, characteristic
4#19151529C211yesmaximal, characteristic
5#19151528C211yesmaximal, characteristic
6#19151519C212yesmaximal
7#19151518C212yesmaximal
8#19151467C212yesmaximal
9#19151462C212yesmaximal
10#19151443C211yesmaximal, characteristic
11#398×C89C211yesmaximal, characteristic
12C22×Dic178C2212yes—
13#15668011—24no—
14#15668002—24no—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2211yescharacteristic
17C2×C4⋊Dic89C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2212yes—
24C2×#13083553C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26C2×C4×Dic89C2212yes—
27#15667919C2212yes—
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C2×Dic178—24no—
38C2×Dic178—42no—
39C2×Dic178—42no—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C4⋊Dic89—22no—
47C4⋊Dic89—22no—
48C4⋊Dic89—42no—
49#13083553—22no—
50#13083553—22no—
51#13083553—22no—
52#13083553—22no—
53#13083553—24no—
54#13083553—42no—
55#13083553—42no—
56C4×Dic89D414yes—
57C4×Dic89Q818yescomplemented
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2312yes—
63C4⋊C4×C89—22no—
64C4⋊C4×C89—22no—
65C4⋊C4×C89—42no—
66C23×C89C2411yescharacteristic
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—21no—
71C2×C4×C89—21no—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89—21no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89C2×D412yes—
79C2×C4×C89C2×Q814yes—
80C2×Dic89—22no—
81C2×Dic89—21no—
82C2×Dic89—21no—
83C2×Dic89—22no—
84C2×Dic89—21no—
85C2×Dic89—21no—
86C2×Dic89—22no—
87C2×Dic89—21no—
88C2×Dic89—22no—
89C2×Dic89—21no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89C2×D412yes—
93C2×Dic89C2×D412yes—
94C2×Dic89C2×Q814yes—
95C2×Dic89C2×Q814yes—
96Dic178—48no—
97C22×C89C22×D411yescharacteristic
98C22×C89C22×Q812yes—
99C22×C89H(5,𝔽2)11yescharacteristic
100C22×C89H(5,𝔽2)11yescharacteristic
101C22×C892−1+412yes—
102C4×C89—22no—
103C4×C89—24no—
104C4×C89—42no—
105C4×C89—41no—
106C4×C89—41no—
107Dic89—22no—
108Dic89—24no—
109Dic89—42no—
110Dic89—41no—
111Dic89—41no—
112Dic89C4⋊Q814yes—
113C2×C89C2×C4⋊Q811yescharacteristic
114C2×C89#53511yescharacteristic
115C2×C89#53611yescharacteristic
116C2×C89#54412yes—
117C2×C89#54412yes—
118#2660—891nomaximal, Sylow
119C89#266011yescharacteristic, complemented, Sylow
120C2×C4⋊Q8—891no—
121C2×#125—891no—
122#398—891no—
123#398—891no—
124#398—891no—
125#398D8911yescharacteristic
126#395—892no—
127#395—892no—
128#384—892no—
129#382—892no—
130#376—891no—
131C22×Q8—892no—
132C4⋊Q8—1784no—
133#125—1784no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4—892no—
136C2×C4⋊C4—892no—
137C2×C4⋊C4—891no—
138C2×C4⋊C4—891no—
139C2×C4⋊C4—891no—
140C2×C4⋊C4—891no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—892no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4C2×D8911yescharacteristic
145C2×C4⋊C4C2×D8911yescharacteristic
146C2×C4⋊C4C2×D8912yes—
147C2×C42—891no—
148C2×C42—892no—
149#95—892no—
150#95—891no—
151#95—892no—
152#95—892no—
153#95—892no—
154#95C2×D8911yescharacteristic
155#95C2×D8912yes—
156C2×Q8—3562no—
157C2×Q8—3562no—
158C2×Q8—1784no—
159C22×C4—891no—
160C22×C4—892no—
161C22×C4—891no—
162C22×C4—891no—
163C22×C4—892no—
164C22×C4—891no—
165C22×C4C22×D8911yescharacteristic
166C22×C4C22×D8912yes—
167C22×C4C22×D8911yescharacteristic
168C22×C4C22×D8911yescharacteristic
169C22×C4C22×D8912yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—3562no—
174C4⋊C4—3562no—
175C4⋊C4—3562no—
176C4⋊C4—1782no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4—1782no—
180C4⋊C4—1784no—
181C4⋊C4—1782no—
182C4⋊C4—1782no—
183C42—894no—
184C42—898no—
185C23C23×D8911yescharacteristic
186Q8—3568no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—892no—
199C2×C4—894no—
200C2×C4—892no—
201C2×C4—894no—
202C2×C4—1781no—
203C2×C4—1781no—
204C2×C4—1782no—
205C2×C4—1781no—
206C2×C4—1782no—
207C2×C4—1781no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4—1781no—
211C2×C4—1782no—
212C2×C4—1781no—
213C2×C4—1782no—
214C2×C4D4×D8912yes—
215C2×C4Q8×D8914yes—
216C22C2×D4×D8911yescharacteristic
217C22C2×Q8×D8912yes—
218C22#1566805711yescharacteristic
219C22#1566805811yescharacteristic
220C22#1566805912yes—
221C4—22no—
222C4—24no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—894no—
227C4—3562no—
228C4—3561no—
229C4—3561no—
230C4—1782no—
231C4—1784no—
232C2C4⋊Q8×D8911yescharacteristic
233C2#1915216411yescharacteristic
234C2#1915217011yescharacteristic
235C2#1915222712yes—
236C2#1915222812yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#398×C89C2
hypercenter#398D89
hypocenterC89#2660
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
57. C4×Dic89Q8semidirect
119. C89#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156680022
#191515302
#191515292
#191515282
#191515192
#191515182
#191514672
#191514622
#191514432
#398×C892
#266089