Finite Group Databasebeta

← #26026419

Subgroups — #26026419

Order 11392.

434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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×#15668007C211yesmaximal, characteristic
2C2×#15668003C211yesmaximal, characteristic, complemented
3#19151533C211yesmaximal, characteristic
4#19151532C212yesmaximal, complemented
5#19151528C211yesmaximal, characteristic, complemented
6#19151525C211yesmaximal, characteristic
7#19151522C212yesmaximal
8#19151495C212yesmaximal, complemented
9#19151490C212yesmaximal
10#19151449C211yesmaximal, characteristic, complemented
11#400×C89C211yesmaximal, characteristic, complemented
12#15668007—24no—
13#15668003—24no—
14C2×C4⋊Dic89C2212yes—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2212yes—
22C2×#13083551C2211yescharacteristic
23C2×#13083551C2212yes—
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2212yes—
27C2×C4×Dic89C2212yes—
28C2×C4×Dic89C2211yescharacteristic
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C22×Dic89C2311yescharacteristic
39C22×Dic89C2312yes—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2312yes—
43C4⋊Dic89—22no—
44C4⋊Dic89—24no—
45C4⋊Dic89—22no—
46#13083553—24no—
47#13083553—22no—
48#13083553—24no—
49#13083553—24no—
50#13083553—42no—
51#13083551—22no—
52#13083551—22no—
53#13083551—22no—
54#13083551—24no—
55#13083551—42no—
56C4×Dic89—42no—
57C4×Dic89D414yes—
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C4⋊C4×C89—22no—
64C4⋊C4×C89—22no—
65C23×C89C2411yescharacteristic
66C22×D89—21no—
67C22×D89—22no—
68C22×D89—21no—
69C22×D89—22no—
70C22×D89—21no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89C2×D412yes—
84C2×Dic89—22no—
85C2×Dic89—21no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—21no—
89C2×Dic89—21no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89C2×D412yes—
95C2×Dic89C2×D412yes—
96C2×Dic89#4114yes—
97C22×C89C22×D411yescharacteristic
98C22×C89C2×#4112yes—
99C22×C89H(5,𝔽2)11yescharacteristic
100C22×C892−1+412yes—
101C22×C892−1+411yescharacteristic
102C2×D89—41no—
103C2×D89—41no—
104C2×D89—41no—
105C2×D89—42no—
106C2×D89—42no—
107C4×C89—22no—
108C4×C89—42no—
109C4×C89—41no—
110C4×C89—41no—
111C4×C89—42no—
112Dic89—22no—
113Dic89—22no—
114Dic89—24no—
115Dic89—41no—
116Dic89—42no—
117C2×C89#53211yescharacteristic
118C2×C89#53611yescharacteristic
119C2×C89#53711yescharacteristic
120C2×C89#53912yes—
121C2×C89#54112yes—
122D89—81no—
123#2664—891nomaximal, Sylow
124C89#266411yescharacteristic, complemented, Sylow
125C2×#126—891no—
126C2×#125—891no—
127#400D8911yescharacteristic, complemented
128#399—891no—
129#398—891no—
130#398—892no—
131#397—891no—
132#396—892no—
133#389—892no—
134#388—892no—
135C4×C4⋊C4—891no—
136#126—1784no—
137#125—1784no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—892no—
140C2×C4⋊C4—892no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—891no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—892no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4C2×D8911yescharacteristic
147C2×C4⋊C4C2×D8911yescharacteristic
148C2×C22⋊C4—892no—
149C2×C22⋊C4—891no—
150C2×C22⋊C4—891no—
151C2×C22⋊C4—891no—
152C2×C22⋊C4—892no—
153C2×C42—891no—
154C2×C42—892no—
155#95—891no—
156#95—892no—
157#95—892no—
158#95C2×D8911yescharacteristic
159#95C2×D8912yes—
160#95C2×D8912yes—
161C24—891no—
162C22×C4—892no—
163C22×C4—891no—
164C22×C4—891no—
165C22×C4—891no—
166C22×C4—892no—
167C22×C4C22×D8911yescharacteristic
168C22×C4C22×D8912yes—
169C22×C4C22×D8911yescharacteristic
170C22×C4C22×D8912yes—
171C22×C4C22×D8911yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—3562no—
175C4⋊C4—1784no—
176C4⋊C4—1784no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4—1784no—
180C4⋊C4—1784no—
181C4⋊C4—1782no—
182C22⋊C4—3562no—
183C22⋊C4—1782no—
184C22⋊C4—1782no—
185C22⋊C4—1784no—
186C22⋊C4—1782no—
187C42—894no—
188C42—3562no—
189C23—1781no—
190C23—1782no—
191C23—1781no—
192C23—1782no—
193C23—1781no—
194C23C23×D8911yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—892no—
208C2×C4—892no—
209C2×C4—894no—
210C2×C4—1781no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4—1781no—
217C2×C4—1782no—
218C2×C4—1782no—
219C2×C4—1781no—
220C2×C4D4×D8912yes—
221C22—3561no—
222C22—3561no—
223C22—3561no—
224C22—3562no—
225C22—3562no—
226C22C2×D4×D8911yescharacteristic
227C22#41×D8912yes—
228C22#1566805811yescharacteristic
229C22#1566805912yes—
230C22#1566806011yescharacteristic
231C4—22no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—42no—
236C4—3561no—
237C4—3562no—
238C4—1782no—
239C4—1782no—
240C4—1784no—
241C2—7121no—
242C2#1915214711yescharacteristic
243C2#1915217011yescharacteristic
244C2#1915217811yescharacteristic
245C2#1915218912yes—
246C2#1915220712yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC23×D89C23
hypercenter#400D89
hypocenterC89#2664
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#15668003C2semidirect
4. #19151532C2semidirect
5. #19151528C2semidirect
8. #19151495C2semidirect
10. #19151449C2semidirect
11. #400×C89C2semidirect
124. C89#2664semidirect
127. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680072
C2×#156680032
#191515332
#191515322
#191515282
#191515252
#191515222
#191514952
#191514902
#191514492
#400×C892
#266489