Finite Group Databasebeta

← #26028322

Subgroups — #26028322

Order 11392.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15668003C211yesmaximal, characteristic
2C2×#15668002C211yesmaximal, characteristic
3#19151540C212yesmaximal
4#19151538C211yesmaximal, characteristic
5#19151537C211yesmaximal, characteristic
6#19151532C212yesmaximal
7#19151531C212yesmaximal
8#19151529C211yesmaximal, characteristic
9#19151529C212yesmaximal
10#19151462C211yesmaximal, characteristic
11#398×C89C211yesmaximal, characteristic
12#15668003—24no—
13#15668002—24no—
14C2×C4⋊Dic89C2212yes—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2212yes—
23C2×#13083553C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C22×Dic89C2312yes—
38C22×Dic89C2311yescharacteristic
39C22×Dic89C2312yes—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C4⋊Dic89—22no—
44C4⋊Dic89—22no—
45C4⋊Dic89—24no—
46#13083553—22no—
47#13083553—22no—
48#13083553—22no—
49#13083553—22no—
50#13083553—24no—
51#13083553—42no—
52#13083553—42no—
53C4×Dic89D414yes—
54C22×C4×C89C2312yes—
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2312yes—
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C4⋊C4×C89—22no—
60C4⋊C4×C89—22no—
61C4⋊C4×C89—42no—
62C23×C89C2411yescharacteristic
63C2×C4×C89—22no—
64C2×C4×C89—21no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89C2×D412yes—
76C2×Dic89—21no—
77C2×Dic89—21no—
78C2×Dic89—22no—
79C2×Dic89—21no—
80C2×Dic89—21no—
81C2×Dic89—22no—
82C2×Dic89—21no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—21no—
86C2×Dic89—22no—
87C2×Dic89—24no—
88C2×Dic89—22no—
89C2×Dic89C2×D412yes—
90C2×Dic89C2×D412yes—
91C22×C89C22×D411yescharacteristic
92C22×C89H(5,𝔽2)11yescharacteristic
93C22×C892−1+412yes—
94C22×C892−1+412yes—
95C22×C892−1+411yescharacteristic
96C4×C89—22no—
97C4×C89—41no—
98C4×C89—41no—
99C4×C89—42no—
100C4×C89—42no—
101Dic89—22no—
102Dic89—22no—
103Dic89—41no—
104Dic89—42no—
105Dic89—41no—
106Dic89—42no—
107C2×C89#53611yescharacteristic
108C2×C89#53611yescharacteristic
109C2×C89#53711yescharacteristic
110C2×C89#56312yes—
111C2×C89#56412yes—
112#2822—891nomaximal, Sylow
113C89#282211yescharacteristic, complemented, Sylow
114C2×#125—891no—
115C2×#125—891no—
116#400—891no—
117#400—891no—
118#400—892no—
119#398—891no—
120#398—892no—
121#398—892no—
122#398—892no—
123#398D8911yescharacteristic
124#382—891no—
125#125—1784no—
126#125—1784no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—892no—
129C2×C4⋊C4—891no—
130C2×C4⋊C4—891no—
131C2×C4⋊C4—892no—
132C2×C4⋊C4—891no—
133C2×C4⋊C4—891no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4—891no—
136C2×C4⋊C4—891no—
137C2×C4⋊C4C2×D8911yescharacteristic
138C2×C4⋊C4C2×D8911yescharacteristic
139C2×C4⋊C4C2×D8912yes—
140C2×C42—891no—
141#95—892no—
142#95—891no—
143#95—892no—
144#95—892no—
145#95—892no—
146#95—892no—
147#95—892no—
148#95C2×D8911yescharacteristic
149#95C2×D8912yes—
150C22×C4—891no—
151C22×C4—891no—
152C22×C4—892no—
153C22×C4—891no—
154C22×C4—892no—
155C22×C4—891no—
156C22×C4C22×D8912yes—
157C22×C4C22×D8911yescharacteristic
158C22×C4C22×D8911yescharacteristic
159C22×C4C22×D8912yes—
160C22×C4C22×D8911yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—3562no—
165C4⋊C4—3562no—
166C4⋊C4—1782no—
167C4⋊C4—1782no—
168C4⋊C4—1784no—
169C4⋊C4—1782no—
170C4⋊C4—1782no—
171C4⋊C4—1784no—
172C4⋊C4—1782no—
173C4⋊C4—1782no—
174C42—894no—
175C23C23×D8911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—892no—
189C2×C4—892no—
190C2×C4—1781no—
191C2×C4—1782no—
192C2×C4—1781no—
193C2×C4—1781no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1781no—
197C2×C4—1782no—
198C2×C4—1784no—
199C2×C4—1782no—
200C2×C4—1781no—
201C2×C4—1781no—
202C2×C4—1782no—
203C2×C4D4×D8912yes—
204C22C2×D4×D8911yescharacteristic
205C22#1566805711yescharacteristic
206C22#1566805912yes—
207C22#1566805911yescharacteristic
208C22#1566806012yes—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—42no—
214C4—3561no—
215C4—3562no—
216C4—3561no—
217C4—3562no—
218C4—1782no—
219C4—1782no—
220C2#1915217011yescharacteristic
221C2#1915217311yescharacteristic
222C2#1915217711yescharacteristic
223C2#1915234912yes—
224C2C89⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#398×C89C2
hypercenter#398D89
hypocenterC89#2822
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
113. C89#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#156680032
C2×#156680022
#191515402
#191515382
#191515372
#191515322
#191515312
#191515292
#191514622
#398×C892
#282289