Finite Group Databasebeta

← #26025277

Subgroups — #26025277

Order 11392.

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

normal subgroups only

This group has 556 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
1C2×#15668011C212yesmaximal
2C2×#15668010C212yesmaximal
3#19151519C212yesmaximal
4#19151518C211yesmaximal, characteristic
5#19151495C212yesmaximal
6#19151493C212yesmaximal
7#19151467C211yesmaximal, characteristic
8#19151449C212yesmaximal
9#395×C89C211yesmaximal, characteristic
10C22×Dic178C2212yes—
11C22×Dic178C2211yescharacteristic
12#15668011—28no—
13#15668010—28no—
14C2×C4⋊Dic89C2212yes—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2212yes—
22C2×C4×Dic89C2212yes—
23C2×C4×Dic89C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2211yescharacteristic
27#15667919C2212yes—
28C22×Q8×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2212yes—
30C2×C4⋊C4×C89C2211yescharacteristic
31#95×C89C2212yes—
32#95×C89C2211yescharacteristic
33C2×Dic178—24no—
34C2×Dic178—24no—
35C2×Dic178—24no—
36C2×Dic178—41no—
37C2×Dic178—42no—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C4⋊Dic89—24no—
43C4⋊Dic89—41no—
44#13083553—24no—
45#13083553—24no—
46#13083553—24no—
47#13083553—24no—
48#13083553D418yes—
49#13083553Q818yescomplemented
50C4×Dic89—24no—
51C4×Dic89—24no—
52C4×Dic89Q814yescomplemented
53C2×Q8×C89—24no—
54C2×Q8×C89—41no—
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2311yescharacteristic
57C22×C4×C89C2312yes—
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2312yes—
60C4⋊C4×C89—24no—
61C4⋊C4×C89—41no—
62C23×C89C2411yescharacteristic
63Q8×C89—44no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—21no—
67C2×C4×C89—22no—
68C2×C4×C89—21no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89—21no—
74C2×C4×C89C2×D414yes—
75C2×C4×C89C2×Q812yes—
76C2×C4×C89C2×Q814yes—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89C2×D414yes—
85C2×Dic89C2×D414yes—
86C2×Dic89C2×Q814yes—
87C2×Dic89C2×Q814yes—
88C2×Dic89C2×Q814yes—
89Dic178—44no—
90Dic178—48no—
91C22×C89C22×D412yes—
92C22×C89C22×Q811yescharacteristic
93C22×C89C22×Q812yes—
94C22×C89H(5,𝔽2)11yescharacteristic
95C22×C892−1+411yescharacteristic
96C4×C89—22no—
97C4×C89—24no—
98C4×C89—24no—
99C4×C89—41no—
100C4×C89—41no—
101Dic89—24no—
102Dic89—24no—
103Dic89—42no—
104Dic89C4⋊Q818yescomplemented
105C2×C89C2×C4⋊Q812yes—
106C2×C89#54411yescharacteristic
107C2×C89D4211yescharacteristic
108C2×C89D4×Q812yes—
109C2×C89Q8211yescharacteristic
110#2551—891nomaximal, Sylow
111C89#255111yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—892no—
113C2×C4⋊Q8—892no—
114#395—891no—
115#395—892no—
116#395D8911yescharacteristic
117#389—892no—
118#389—892no—
119#384—891no—
120C4×C4⋊C4—892no—
121C22×Q8—891no—
122C22×Q8—892no—
123C22×Q8C2×D8911yescharacteristic
124C4⋊Q8—1788no—
125C4⋊Q8—1788no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—891no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4—892no—
131C2×C4⋊C4—892no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—892no—
134C2×C4⋊C4C2×D8912yes—
135C2×C4⋊C4C2×D8911yescharacteristic
136C2×C42—891no—
137C2×C42—892no—
138C2×C42—892no—
139#95—892no—
140#95—891no—
141#95—892no—
142#95C2×D8912yes—
143#95C2×D8911yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—3562no—
147C2×Q8—3561no—
148C2×Q8—1784no—
149C2×Q8—1784no—
150C2×Q8—1784no—
151C22×C4—892no—
152C22×C4—892no—
153C22×C4—892no—
154C22×C4—892no—
155C22×C4C22×D8911yescharacteristic
156C22×C4C22×D8911yescharacteristic
157C22×C4C22×D8912yes—
158C22×C4C22×D8911yescharacteristic
159C22×C4C22×D8912yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—898no—
163C4⋊C4—898no—
164C4⋊C4—3561no—
165C4⋊C4—1784no—
166C4⋊C4—1784no—
167C4⋊C4—1784no—
168C4⋊C4—1784no—
169C4⋊C4—1784no—
170C42—894no—
171C42—1784no—
172C42—1784no—
173C23C23×D8911yescharacteristic
174Q8—44no—
175Q8—3568no—
176Q8—3564no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—894no—
188C2×C4—894no—
189C2×C4—894no—
190C2×C4—894no—
191C2×C4—894no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4D4×D8914yes—
200C2×C4Q8×D8912yes—
201C2×C4Q8×D8914yes—
202C22C2×D4×D8912yes—
203C22C2×Q8×D8911yescharacteristic
204C22C2×Q8×D8912yes—
205C22#1566805711yescharacteristic
206C22#1566805911yescharacteristic
207C4—22no—
208C4—24no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—898no—
213C4—3562no—
214C4—1784no—
215C4—1784no—
216C2C4⋊Q8×D8912yes—
217C2#1915222711yescharacteristic
218C2#1915223011yescharacteristic
219C2#1915226112yes—
220C2#1915232811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#395×C89C2
hypercenter#395D89
hypocenterC89#2551
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
49. #13083553Q8semidirect
52. C4×Dic89Q8semidirect
104. Dic89C4⋊Q8semidirect
111. C89#2551semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156680102
#191515192
#191515182
#191514952
#191514932
#191514672
#191514492
#395×C892
#255189