Finite Group Databasebeta

← #26026596

Subgroups — #26026596

Order 11392.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15667997C212yesmaximal
2C2×#15667988C212yesmaximal, complemented
3#19151531C212yesmaximal, complemented
4#19151527C212yesmaximal, complemented
5#19151515C211yesmaximal, characteristic
6#19151490C212yesmaximal, complemented
7#19151472C212yesmaximal, complemented
8#19151467C211yesmaximal, characteristic, complemented
9#395×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C22×C4×D89C2212yes—
12#15667997—28no—
13#15667988—28no—
14C2×C4⋊Dic89C2212yes—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2212yes—
27#15667919C2211yescharacteristic
28C22×Q8×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2212yes—
30C2×C4⋊C4×C89C2211yescharacteristic
31#95×C89C2212yes—
32#95×C89C2211yescharacteristic
33C23×D89C2312yes—
34C2×D356—24no—
35C2×D356—41no—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C2×C4×D89—24no—
40C2×C4×D89—24no—
41C2×C4×D89—42no—
42C4⋊Dic89—24no—
43C4⋊Dic89—41no—
44#13083553—24no—
45#13083553—24no—
46#13083553—24no—
47#13083551—24no—
48#13083551—24no—
49#13083551—24no—
50#13083551—24no—
51#13083551D418yes—
52C4×Dic89—22no—
53C2×Q8×C89—24no—
54C2×Q8×C89—41no—
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2312yes—
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C4⋊C4×C89—24no—
61C4⋊C4×C89—41no—
62C23×C89C2411yescharacteristic
63C22×D89—22no—
64C22×D89—22no—
65C22×D89—22no—
66C22×D89—22no—
67C22×D89—22no—
68C22×D89—22no—
69C22×D89C2×D414yes—
70Q8×C89—44no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89C2×D414yes—
83C2×C4×C89#4112yes—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89C2×D414yes—
93D356—44no—
94C4×D89—48no—
95C22×C89C22×D412yes—
96C22×C89C2×#4111yescharacteristic
97C22×C89H(5,𝔽2)11yescharacteristic
98C22×C892−1+411yescharacteristic
99C22×C892−1+412yes—
100C2×D89—24no—
101C2×D89—24no—
102C2×D89—24no—
103C2×D89—42no—
104C2×D89—42no—
105C2×D89—42no—
106C2×D89—42no—
107C4×C89—22no—
108C4×C89—24no—
109C4×C89—42no—
110C4×C89—41no—
111C4×C89—41no—
112Dic89—24no—
113Dic89—42no—
114Dic89—42no—
115C2×C89#53612yes—
116C2×C89#53911yescharacteristic
117C2×C89D4211yescharacteristic
118C2×C89#54712yes—
119C2×C89#56311yescharacteristic
120D89—44no—
121#2680—891nomaximal, Sylow
122C89#268011yescharacteristic, complemented, Sylow
123C2×#123—892no—
124C2×C22⋊Q8—892no—
125#398—892no—
126#397—892no—
127#395D8911yescharacteristic, complemented
128#394—891no—
129#388—892no—
130#385—892no—
131#384—891no—
132C22×Q8C2×D8911yescharacteristic
133C22×D4—891no—
134C23×C4—892no—
135#123—1788no—
136C22⋊Q8—1788no—
137C2×C4⋊C4—891no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—892no—
140C2×C4⋊C4—892no—
141C2×C4⋊C4—892no—
142C2×C4⋊C4C2×D8912yes—
143C2×C4⋊C4C2×D8911yescharacteristic
144C2×C22⋊C4—892no—
145C2×C22⋊C4—892no—
146C2×C22⋊C4—892no—
147C2×C22⋊C4—892no—
148C2×C22⋊C4—892no—
149C2×C42—891no—
150#95—892no—
151#95—892no—
152#95—891no—
153#95C2×D8912yes—
154#95C2×D8911yescharacteristic
155C24—892no—
156C2×Q8—24no—
157C2×Q8—41no—
158C2×D4—3561no—
159C2×D4—1784no—
160C22×C4—892no—
161C22×C4—892no—
162C22×C4—892no—
163C22×C4—3562no—
164C22×C4—1784no—
165C22×C4—1784no—
166C22×C4C22×D8912yes—
167C22×C4C22×D8911yescharacteristic
168C22×C4C22×D8911yescharacteristic
169C22×C4C22×D8912yes—
170C22×C4C22×D8911yescharacteristic
171C4⋊C4—24no—
172C4⋊C4—41no—
173C4⋊C4—3561no—
174C4⋊C4—1784no—
175C4⋊C4—1784no—
176C4⋊C4—1784no—
177C4⋊C4—1784no—
178C22⋊C4—898no—
179C22⋊C4—1784no—
180C22⋊C4—1784no—
181C22⋊C4—1784no—
182C22⋊C4—1784no—
183C42—1782no—
184C23—894no—
185C23—1782no—
186C23—1782no—
187C23—1782no—
188C23—1782no—
189C23—1782no—
190C23—1782no—
191C23C23×D8911yescharacteristic
192Q8—44no—
193D4—3564no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—894no—
206C2×C4—3568no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4—1782no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4D4×D8914yes—
216C2×C4#1308357512yes—
217C22—3562no—
218C22—3562no—
219C22—3562no—
220C22—3562no—
221C22—1784no—
222C22—1784no—
223C22—1784no—
224C22C2×D4×D8912yes—
225C22C2×#1308357511yescharacteristic
226C22#1566805711yescharacteristic
227C22#1566805911yescharacteristic
228C22#1566806012yes—
229C4—22no—
230C4—24no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—3562no—
235C4—3562no—
236C4—1784no—
237C2—3564no—
238C2#1915217112yes—
239C2#1915219711yescharacteristic
240C2#1915223011yescharacteristic
241C2#1915225112yes—
242C2#1915234711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#395×C89C2
prime radicalC22×D356C22
hypercenter#395D89
hypocenterC89#2680
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#15667988C2semidirect
3. #19151531C2semidirect
4. #19151527C2semidirect
6. #19151490C2semidirect
7. #19151472C2semidirect
8. #19151467C2semidirect
9. #395×C89C2semidirect
122. C89#2680semidirect
127. #395D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679972
C2×#156679882
#191515312
#191515272
#191515152
#191514902
#191514722
#191514672
#395×C892
#268089