Finite Group Databasebeta

← #26027953

Subgroups — #26027953

Order 11392.

472 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#19151537C211yesmaximal, characteristic, complemented
2#19151521C212yesmaximal, complemented
3#19151518C211yesmaximal, characteristic, complemented
4#19151510C212yesmaximal, complemented
5#19151482C212yesmaximal, complemented
6#19151478C212yesmaximal
7#19151470C212yesmaximal, complemented
8#19151456C212yesmaximal, complemented
9#390×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C23×Dic89C2212yes—
12C2×C4⋊Dic89C2211yescharacteristic
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C22⋊Dic89C2212yes—
17C2×C22⋊Dic89C2212yes—
18C2×C22⋊Dic89C2212yes—
19#15667919C2211yescharacteristic
20#15667919C2212yes—
21#15667919C2211yescharacteristic
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26C22×D4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2212yes—
30C2×C42×C89C2211yescharacteristic
31C2×Dic178—41no—
32C2×Dic178—42no—
33C22×Dic89—24no—
34C22×Dic89—42no—
35C22×Dic89—42no—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C4⋊Dic89—41no—
41#13083553—24no—
42#13083553—42no—
43#13083553—42no—
44C22⋊Dic89—24no—
45C22⋊Dic89—42no—
46C22⋊Dic89—42no—
47C24×C89C2312yes—
48C2×D4×C89—41no—
49C2×D4×C89—41no—
50C2×D4×C89Q814yescomplemented
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22×C4×C89C2311yescharacteristic
54C22×C4×C89C2311yescharacteristic
55C4⋊C4×C89—41no—
56C22⋊C4×C89—42no—
57C22⋊C4×C89—42no—
58C42×C89—41no—
59C23×C89—22no—
60C23×C89—22no—
61C23×C89—22no—
62C23×C89—22no—
63C23×C89—22no—
64C23×C89—22no—
65C23×C89C2×Q814yes—
66C23×C89C2411yescharacteristic
67D4×C89—44no—
68C2×C4×C89—21no—
69C2×C4×C89—21no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—21no—
76C2×C4×C89—21no—
77C2×C4×C89C2×Q812yes—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—48no—
90C2×Dic89#4114yes—
91Dic178—44no—
92C22×C89—24no—
93C22×C89—24no—
94C22×C89—24no—
95C22×C89—42no—
96C22×C89—42no—
97C22×C89—42no—
98C22×C89—42no—
99C22×C89C22×Q811yescharacteristic
100C22×C89C2×#4112yes—
101C22×C89H(5,𝔽2)11yescharacteristic
102C22×C89H(5,𝔽2)12yes—
103C22×C89H(5,𝔽2)11yescharacteristic
104C4×C89—22no—
105C4×C89—42no—
106C4×C89—41no—
107C4×C89—41no—
108Dic89—24no—
109Dic89—42no—
110Dic89—42no—
111Dic89—42no—
112C2×C89—44no—
113C2×C89#53812yes—
114C2×C89#54311yescharacteristic
115C2×C89#55412yes—
116C2×C89#55511yescharacteristic
117C2×C89#56011yescharacteristic
118#2784—891nomaximal, Sylow
119C89#278411yescharacteristic, complemented, Sylow
120#400—891no—
121#396—892no—
122#395—891no—
123#393—892no—
124#390D8911yescharacteristic
125#387—892no—
126#386—892no—
127#385—892no—
128#380—892no—
129C22×Q8—891no—
130C22×D4C2×D8911yescharacteristic
131C23×C4—892no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—892no—
134C2×C4⋊C4—891no—
135C2×C4⋊C4—892no—
136C2×C4⋊C4C2×D8911yescharacteristic
137C2×C22⋊C4—892no—
138C2×C22⋊C4—892no—
139C2×C22⋊C4—892no—
140C2×C22⋊C4C2×D8912yes—
141C2×C22⋊C4C2×D8912yes—
142C2×C42C2×D8911yescharacteristic
143#95—891no—
144#95—892no—
145#95—891no—
146#95—892no—
147#95—892no—
148#95—892no—
149#95—892no—
150C24C22×D8912yes—
151C2×Q8—3562no—
152C2×Q8—3561no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4Dic17814yescomplemented
156C22×C4—892no—
157C22×C4—892no—
158C22×C4—892no—
159C22×C4—892no—
160C22×C4—3562no—
161C22×C4—3562no—
162C22×C4—1784no—
163C22×C4C22×D8911yescharacteristic
164C22×C4C22×D8912yes—
165C22×C4C22×D8911yescharacteristic
166C22×C4C22×D8911yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—3562no—
169C4⋊C4—3562no—
170C4⋊C4—3561no—
171C4⋊C4—1784no—
172C22⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—3562no—
175C22⋊C4—3562no—
176C22⋊C4—1784no—
177C42—41no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23C2×Dic17814yes—
185C23C23×D8911yescharacteristic
186Q8—3564no—
187D4—44no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—894no—
198C2×C4—3568no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4C2×Dic17812yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22C22×Dic17811yescharacteristic
219C22#41×D8912yes—
220C22#1566805711yescharacteristic
221C22#1566805712yes—
222C22#1566805711yescharacteristic
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—3562no—
228C4—3562no—
229C4—3562no—
230C4—1784no—
231C2—44no—
232C2#1915218012yes—
233C2#1915222411yescharacteristic
234C2#1915230712yes—
235C2#1915231011yescharacteristic
236C2#1915233511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#390×C89C2
prime radicalC22×D4×C89C22
hypercenter#390D89
hypocenterC89#2784
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #19151537C2semidirect
2. #19151521C2semidirect
3. #19151518C2semidirect
4. #19151510C2semidirect
5. #19151482C2semidirect
7. #19151470C2semidirect
8. #19151456C2semidirect
50. C2×D4×C89Q8semidirect
119. C89#2784semidirect
155. C2×D4Dic178semidirect

Maximal subgroups

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

subgroupindex
#191515372
#191515212
#191515182
#191515102
#191514822
#191514782
#191514702
#191514562
#390×C892
#278489