Finite Group Databasebeta

← #26025501

Subgroups — #26025501

Order 11392.

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

normal subgroups only

This group has 476 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
1#19151537C211yesmaximal, characteristic, complemented
2#19151515C211yesmaximal, characteristic
3#19151509C212yesmaximal, complemented
4#19151490C212yesmaximal, complemented
5#19151476C212yesmaximal
6#19151465C212yesmaximal, complemented
7#19151460C212yesmaximal, complemented
8C4×#13083551C212yesmaximal, complemented
9#391×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C22×C4×D89C2212yes—
12C2×C4⋊Dic89C2211yescharacteristic
13C2×#13083551C2212yes—
14C2×#13083551C2212yes—
15C2×#13083551C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×C4×Dic89C2212yes—
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2211yescharacteristic
22#15667919C2212yes—
23#15667919C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2212yes—
26C22×Q8×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C42×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2212yes—
31C23×D89C2312yes—
32C2×D356—24no—
33C2×D356—41no—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C2×C4×D89—24no—
38C2×C4×D89—24no—
39C2×C4×D89—42no—
40C4⋊Dic89—41no—
41#13083551—24no—
42#13083551—24no—
43#13083551—24no—
44#13083551—42no—
45#13083551—42no—
46C4×Dic89—24no—
47C2×Q8×C89—22no—
48C2×Q8×C89—41no—
49C2×Q8×C89—41no—
50C22×C4×C89C2311yescharacteristic
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C4⋊C4×C89—41no—
56C42×C89—41no—
57C23×C89C2411yescharacteristic
58C22×D89—22no—
59C22×D89—22no—
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89#4114yes—
65Q8×C89—44no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—21no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89#4112yes—
78C2×C4×C89#4114yes—
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—
88D356—44no—
89C4×D89—48no—
90C22×C89C2×#4111yescharacteristic
91C22×C89C2×#4112yes—
92C22×C89C2×#4112yes—
93C22×C89H(5,𝔽2)11yescharacteristic
94C22×C89H(5,𝔽2)11yescharacteristic
95C2×D89—24no—
96C2×D89—24no—
97C2×D89—24no—
98C2×D89—42no—
99C2×D89—42no—
100C2×D89—42no—
101C2×D89—42no—
102C4×C89—22no—
103C4×C89—24no—
104C4×C89—42no—
105C4×C89—41no—
106C4×C89—41no—
107Dic89—42no—
108Dic89—42no—
109Dic89—42no—
110C2×C89#52912yes—
111C2×C89#53811yescharacteristic
112C2×C89#55112yes—
113C2×C89#55111yescharacteristic
114C2×C89#55511yescharacteristic
115D89—44no—
116#2572—891nomaximal, Sylow
117C89#257211yescharacteristic, complemented, Sylow
118#400—891no—
119#394—891no—
120#393—892no—
121#391D8911yescharacteristic, complemented
122#388—892no—
123#386—892no—
124#383—892no—
125#381—892no—
126C4×C22⋊C4—892no—
127C22×Q8C2×D8911yescharacteristic
128C22×D4—891no—
129C23×C4—892no—
130C2×C4⋊C4—891no—
131C2×C4⋊C4C2×D8911yescharacteristic
132C2×C22⋊C4—892no—
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4—892no—
136C2×C22⋊C4—892no—
137C2×C42—892no—
138C2×C42C2×D8911yescharacteristic
139#95—892no—
140#95—892no—
141#95—891no—
142#95—892no—
143#95—891no—
144#95—892no—
145#95—892no—
146#95C2×D8912yes—
147#95C2×D8912yes—
148C24—892no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×D4—3561no—
153C2×D4—1784no—
154C22×C4—892no—
155C22×C4—892no—
156C22×C4—892no—
157C22×C4—3562no—
158C22×C4—1784no—
159C22×C4—1784no—
160C22×C4C22×D8911yescharacteristic
161C22×C4C22×D8912yes—
162C22×C4C22×D8911yescharacteristic
163C22×C4C22×D8911yescharacteristic
164C22×C4C22×D8912yes—
165C4⋊C4—41no—
166C4⋊C4—3561no—
167C22⋊C4—3562no—
168C22⋊C4—3562no—
169C22⋊C4—1784no—
170C22⋊C4—1784no—
171C22⋊C4—1784no—
172C42—41no—
173C42—1784no—
174C23—894no—
175C23—1782no—
176C23—1782no—
177C23—1782no—
178C23—1782no—
179C23—1782no—
180C23—1782no—
181C23C23×D8911yescharacteristic
182Q8—44no—
183D4—3564no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—3568no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4#1308357412yes—
206C2×C4#1308357514yes—
207C22—3562no—
208C22—3562no—
209C22—3562no—
210C22—3562no—
211C22—1784no—
212C22—1784no—
213C22—1784no—
214C22#41×D8912yes—
215C22C2×#1308357411yescharacteristic
216C22C2×#1308357512yes—
217C22#1566805711yescharacteristic
218C22#1566805711yescharacteristic
219C4—22no—
220C4—24no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—3562no—
225C4—3562no—
226C4—3562no—
227C2—3564no—
228C2#1915213512yes—
229C2#1915218611yescharacteristic
230C2#1915227512yes—
231C2#1915227811yescharacteristic
232C2#1915231411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#391×C89C2
prime radicalC22×D356C22
hypercenter#391D89
hypocenterC89#2572
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #19151537C2semidirect
3. #19151509C2semidirect
4. #19151490C2semidirect
6. #19151465C2semidirect
7. #19151460C2semidirect
8. C4×#13083551C2semidirect
9. #391×C89C2semidirect
117. C89#2572semidirect
121. #391D89semidirect

Maximal subgroups

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

subgroupindex
#191515372
#191515152
#191515092
#191514902
#191514762
#191514652
#191514602
C4×#130835512
#391×C892
#257289