Finite Group Databasebeta

← #26026119

Subgroups — #26026119

Order 11392.

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

normal subgroups only

This group has 512 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×#15668002C211yesmaximal, characteristic, complemented
2C2×D4×Dic89C211yesmaximal, characteristic
3#19151534C212yesmaximal, complemented
4#19151530C211yesmaximal, characteristic, complemented
5#19151528C211yesmaximal, characteristic, complemented
6#19151526C212yesmaximal, complemented
7#19151512C211yesmaximal, characteristic
8#19151473C212yesmaximal, complemented
9#19151470C212yesmaximal, complemented
10#19151465C211yesmaximal, characteristic, complemented
11#394×C89C211yesmaximal, characteristic
12C23×Dic89C2212yes—
13#15668002—24no—
14D4×Dic89—24no—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2211yescharacteristic
17C2×C4⋊Dic89C2212yes—
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2212yes—
23C2×C22⋊Dic89C2212yes—
24C2×C22⋊Dic89C2212yes—
25C2×C22⋊Dic89C2212yes—
26C2×C4×Dic89C2211yescharacteristic
27#15667919C2212yes—
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C22×D4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2212yes—
35C2×C22⋊C4×C89C2212yes—
36#95×C89C2211yescharacteristic
37C22×Dic89—24no—
38C22×Dic89—42no—
39C22×Dic89—42no—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
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—42no—
54C22⋊Dic89—24no—
55C22⋊Dic89—24no—
56C22⋊Dic89—42no—
57C4×Dic89D414yes—
58C24×C89C2312yes—
59C2×D4×C89—24no—
60C2×D4×C89—22no—
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2311yescharacteristic
65C4⋊C4×C89—22no—
66C22⋊C4×C89—24no—
67C22⋊C4×C89—42no—
68C23×C89—22no—
69C23×C89—22no—
70C23×C89—22no—
71C23×C89—22no—
72C23×C89—22no—
73C23×C89—22no—
74C23×C89#4114yes—
75C23×C89C2411yescharacteristic
76D4×C89—28no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89—22no—
84C2×C4×C89—21no—
85C2×C4×C89—22no—
86C2×C4×C89C2×D412yes—
87C2×Dic89—21no—
88C2×Dic89—21no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—21no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—21no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—48no—
102C2×Dic89C2×D412yes—
103C2×Dic89C2×D412yes—
104C22×C89—24no—
105C22×C89—24no—
106C22×C89—24no—
107C22×C89—42no—
108C22×C89—42no—
109C22×C89—42no—
110C22×C89—42no—
111C22×C89C22×D411yescharacteristic
112C22×C89C2×#4112yes—
113C22×C89H(5,𝔽2)11yescharacteristic
114C22×C89H(5,𝔽2)11yescharacteristic
115C22×C892−1+412yes—
116C4×C89—22no—
117C4×C89—41no—
118C4×C89—41no—
119C4×C89—42no—
120Dic89—22no—
121Dic89—22no—
122Dic89—41no—
123Dic89—41no—
124Dic89—42no—
125Dic89—42no—
126C2×C89—44no—
127C2×C89#52511yescharacteristic
128C2×C89#53511yescharacteristic
129C2×C89#53611yescharacteristic
130C2×C89#53912yes—
131C2×C89#53912yes—
132#2633—891nomaximal, Sylow
133C89#263311yescharacteristic, complemented, Sylow
134C2×#125—891no—
135C2×C4×D4—891no—
136#399—892no—
137#398—891no—
138#398—891no—
139#397—892no—
140#394—891no—
141#394D8911yescharacteristic
142#385—892no—
143#385—892no—
144#383—891no—
145C22×D4C2×D8911yescharacteristic
146C23×C4—892no—
147#125—1784no—
148C4×D4—1784no—
149C2×C4⋊C4—892no—
150C2×C4⋊C4—892no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4—891no—
155C2×C4⋊C4—891no—
156C2×C4⋊C4—891no—
157C2×C4⋊C4C2×D8911yescharacteristic
158C2×C22⋊C4—892no—
159C2×C22⋊C4—892no—
160C2×C22⋊C4—892no—
161C2×C22⋊C4C2×D8912yes—
162C2×C22⋊C4C2×D8912yes—
163C2×C42—891no—
164#95—892no—
165#95—891no—
166#95—892no—
167#95—892no—
168#95—892no—
169#95C2×D8911yescharacteristic
170C24C22×D8912yes—
171C2×D4—24no—
172C2×D4—22no—
173C22×C4—891no—
174C22×C4—891no—
175C22×C4—892no—
176C22×C4—891no—
177C22×C4—892no—
178C22×C4—891no—
179C22×C4—3562no—
180C22×C4—3562no—
181C22×C4—1784no—
182C22×C4C22×D8912yes—
183C22×C4C22×D8911yescharacteristic
184C22×C4C22×D8911yescharacteristic
185C22×C4C22×D8911yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—3562no—
188C4⋊C4—3562no—
189C4⋊C4—1782no—
190C4⋊C4—1782no—
191C4⋊C4—1782no—
192C4⋊C4—1782no—
193C4⋊C4—1782no—
194C4⋊C4—1782no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—3562no—
198C22⋊C4—1784no—
199C22⋊C4—1784no—
200C42—894no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#1308357314yes—
208C23C23×D8911yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—892no—
220C2×C4—892no—
221C2×C4—3568no—
222C2×C4—1782no—
223C2×C4—1781no—
224C2×C4—1781no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4—1781no—
228C2×C4—1782no—
229C2×C4—1781no—
230C2×C4—1782no—
231C2×C4—1782no—
232C2×C4—1782no—
233C2×C4—1781no—
234C2×C4—1781no—
235C2×C4—1782no—
236C2×C4D4×D8912yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D8911yescharacteristic
245C22C2×#1308357312yes—
246C22#1566805711yescharacteristic
247C22#1566805811yescharacteristic
248C22#1566805912yes—
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—3562no—
254C4—3561no—
255C4—3562no—
256C4—3561no—
257C4—1782no—
258C4—1782no—
259C2—44no—
260C2#1915210411yescharacteristic
261C2#1915216411yescharacteristic
262C2#1915216811yescharacteristic
263C2#1915219212yes—
264C2#1915219312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#394×C89C2
prime radicalC22×D4×C89C22
hypercenter#394D89
hypocenterC89#2633
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#15668002C2semidirect
3. #19151534C2semidirect
4. #19151530C2semidirect
5. #19151528C2semidirect
6. #19151526C2semidirect
8. #19151473C2semidirect
9. #19151470C2semidirect
10. #19151465C2semidirect
133. C89#2633semidirect

Maximal subgroups

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

subgroupindex
C2×#156680022
C2×D4×Dic892
#191515342
#191515302
#191515282
#191515262
#191515122
#191514732
#191514702
#191514652
#394×C892
#263389