Finite Group Databasebeta

← #26024708

Subgroups — #26024708

Order 11392.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15667992C211yesmaximal, characteristic
2C2×#15667970C211yesmaximal, characteristic
3#19151527C214yesmaximal
4#19151504C211yesmaximal, characteristic, complemented
5#19151503C211yesmaximal, characteristic, complemented
6#19151485C214yesmaximal, complemented
7#19151467C211yesmaximal, characteristic, complemented
8C4×#13083551C211yesmaximal, characteristic
9#382×C89C211yesmaximal, characteristic, complemented
10C22×Dic178C2211yescharacteristic
11C22×C4×D89C2211yescharacteristic
12#15667992—24no—
13#15667970—24no—
14C2×C4⋊Dic89C2211yescharacteristic
15C2×C4⋊Dic89C2212yes—
16C2×#13083553C2214yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×C4×Dic89C2211yescharacteristic
21C2×C4×Dic89C2212yes—
22#15667919C2212yes—
23#15667919C2214yes—
24#15667919C2214yes—
25C2×C4⋊C4×C89C2211yescharacteristic
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C42×C89C2211yescharacteristic
28#95×C89C2214yes—
29C23×D89C2311yescharacteristic
30C2×Dic178—22no—
31C2×Dic178—22no—
32C2×Dic178—22no—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C22×Dic89C2311yescharacteristic
36C22×Dic89C2312yes—
37C2×C4×D89—22no—
38C2×C4×D89—22no—
39C2×C4×D89D414yes—
40C4⋊Dic89—22no—
41C4⋊Dic89—24no—
42#13083553—28no—
43#13083551—24no—
44#13083551—24no—
45#13083551—24no—
46C4×Dic89—22no—
47C4×Dic89—24no—
48C22×C4×C89C2312yes—
49C22×C4×C89C2312yes—
50C22×C4×C89C2312yes—
51C22×C4×C89C2311yescharacteristic
52C4⋊C4×C89—22no—
53C4⋊C4×C89—22no—
54C42×C89—22no—
55C23×C89C2411yescharacteristic
56C22×D89—22no—
57C22×D89—21no—
58C22×D89—21no—
59C22×D89—22no—
60C22×D89C2×D412yes—
61C2×C4×C89—22no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—24no—
66C2×C4×C89—24no—
67C2×C4×C89—22no—
68C2×C4×C89C2×D412yes—
69C2×C4×C89#4112yes—
70C2×C4×C89#4112yes—
71C2×Dic89—22no—
72C2×Dic89—21no—
73C2×Dic89—21no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—24no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89C2×D412yes—
81C2×Dic89#4114yes—
82C4×D89—28no—
83Dic178—44no—
84C22×C89C22×D411yescharacteristic
85C22×C89C2×#4111yescharacteristic
86C22×C89C2×#4111yescharacteristic
87C22×C89C2×#4112yes—
88C22×C892−1+412yes—
89C2×D89—22no—
90C2×D89—22no—
91C2×D89—22no—
92C2×D89—42no—
93C2×D89—42no—
94C4×C89—42no—
95C4×C89—42no—
96C4×C89—42no—
97C4×C89#12314yes—
98Dic89—22no—
99Dic89—24no—
100Dic89—42no—
101Dic89—42no—
102C2×C89C2×#12311yescharacteristic
103C2×C89#53211yescharacteristic
104C2×C89#53611yescharacteristic
105C2×C89#55212yes—
106C2×C89#55612yes—
107D89—42no—
108#2499—891nomaximal, Sylow
109C89#249911yescharacteristic, complemented, Sylow
110C2×C22⋊Q8—891no—
111C2×#117—891no—
112#397—894no—
113#391—891no—
114#391—891no—
115#387—894no—
116#384—891no—
117#382D8911yescharacteristic, complemented
118C4×C22⋊C4—891no—
119C22×Q8—891no—
120C23×C4—891no—
121C22⋊Q8—1784no—
122#117—1784no—
123C2×C4⋊C4—891no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4—894no—
126C2×C4⋊C4C2×D8911yescharacteristic
127C2×C4⋊C4C2×D8911yescharacteristic
128C2×C22⋊C4—892no—
129C2×C22⋊C4—892no—
130C2×C22⋊C4—892no—
131C2×C42—892no—
132C2×C42—891no—
133C2×C42C2×D8911yescharacteristic
134#95—892no—
135#95—894no—
136#95—894no—
137#95C2×D8914yes—
138C24—891no—
139C2×Q8—1782no—
140C2×Q8—1782no—
141C2×Q8—1782no—
142C22×C4—892no—
143C22×C4—891no—
144C22×C4—894no—
145C22×C4—892no—
146C22×C4—892no—
147C22×C4—1782no—
148C22×C4—1782no—
149C22×C4C22×D8912yes—
150C22×C4C22×D8912yes—
151C22×C4C22×D8912yes—
152C22×C4C22×D8911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—1784no—
156C4⋊C4—1788no—
157C4⋊C4—1782no—
158C22⋊C4—1784no—
159C22⋊C4—1784no—
160C22⋊C4—1784no—
161C42—22no—
162C42—1784no—
163C42—1782no—
164C23—892no—
165C23—1782no—
166C23—1781no—
167C23—1781no—
168C23—1782no—
169C23C23×D8911yescharacteristic
170Q8—3564no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—892no—
179C2×C4—894no—
180C2×C4—1782no—
181C2×C4—1782no—
182C2×C4—1784no—
183C2×C4—1782no—
184C2×C4—1782no—
185C2×C4—1781no—
186C2×C4—1782no—
187C2×C4—1781no—
188C2×C4—1782no—
189C2×C4—1788no—
190C2×C4D4×D8912yes—
191C2×C4#1308357412yes—
192C2×C4#1308357512yes—
193C22—3562no—
194C22—3562no—
195C22—1782no—
196C22—1782no—
197C22—1782no—
198C22C2×D4×D8911yescharacteristic
199C22#41×D8912yes—
200C22C2×#1308357411yescharacteristic
201C22C2×#1308357511yescharacteristic
202C22#1566805912yes—
203C4—42no—
204C4—42no—
205C4—42no—
206C4—3562no—
207C4—3562no—
208C4—1784no—
209C4—1782no—
210C4#1566799714yes—
211C2—3562no—
212C2C2×#1566799711yescharacteristic
213C2#1915214711yescharacteristic
214C2#1915216811yescharacteristic
215C2#1915228612yes—
216C2#1915231612yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#382×C89C2
prime radicalC23×D89C23
hypercenter#382D89
hypocenterC89#2499
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
4. #19151504C2semidirect
5. #19151503C2semidirect
6. #19151485C2semidirect
7. #19151467C2semidirect
9. #382×C89C2semidirect
109. C89#2499semidirect
117. #382D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679922
C2×#156679702
#191515272
#191515042
#191515032
#191514852
#191514672
C4×#130835512
#382×C892
#249989