Finite Group Databasebeta

← #26028514

Subgroups — #26028514

Order 11392.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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#19151539C212yesmaximal, complemented
2#19151531C212yesmaximal, complemented
3#19151528C212yesmaximal, complemented
4#19151521C212yesmaximal
5#19151518C212yesmaximal, complemented
6#19151510C211yesmaximal, characteristic
7#19151459C211yesmaximal, characteristic
8#19151456C212yesmaximal
9#399×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C23×Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2212yes—
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×C22⋊Dic89C2212yes—
18C2×C22⋊Dic89C2211yescharacteristic
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2212yes—
26C2×C4⋊C4×C89C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2211yescharacteristic
30#95×C89C2211yescharacteristic
31C2×Dic178—42no—
32C2×Dic178—41no—
33C22×Dic89—41no—
34C22×Dic89—41no—
35C22×Dic89Q814yescomplemented
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C4⋊Dic89—42no—
41#13083553—42no—
42#13083553—42no—
43#13083553—42no—
44#13083553—42no—
45C22⋊Dic89—41no—
46C22⋊Dic89—42no—
47C24×C89C2311yescharacteristic
48C22×C4×C89C2311yescharacteristic
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C22×C4×C89C2312yes—
52C4⋊C4×C89—41no—
53C4⋊C4×C89—42no—
54C22⋊C4×C89—42no—
55C22⋊C4×C89—41no—
56C23×C89—22no—
57C23×C89—21no—
58C23×C89—21no—
59C23×C89—22no—
60C23×C89C2×Q812yes—
61C23×C89C2411yescharacteristic
62C2×C4×C89—22no—
63C2×C4×C89—21no—
64C2×C4×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×Dic89—22no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—44no—
84C2×Dic89C2×Q814yes—
85Dic178—44no—
86C22×C89—22no—
87C22×C89—24no—
88C22×C89—41no—
89C22×C89—42no—
90C22×C89—41no—
91C22×C89C22×Q811yescharacteristic
92C22×C89H(5,𝔽2)11yescharacteristic
93C22×C89H(5,𝔽2)11yescharacteristic
94C22×C89H(5,𝔽2)12yes—
95C22×C892−1+412yes—
96C4×C89—41no—
97C4×C89—42no—
98C4×C89—42no—
99C4×C89—41no—
100Dic89—24no—
101Dic89—42no—
102Dic89—42no—
103Dic89—42no—
104C2×C89—42no—
105C2×C89#54311yescharacteristic
106C2×C89#54412yes—
107C2×C89#56011yescharacteristic
108C2×C89#56212yes—
109C2×C89#56311yescharacteristic
110#2841—891nomaximal, Sylow
111C89#284111yescharacteristic, complemented, Sylow
112#400—892no—
113#399D8911yescharacteristic
114#398—892no—
115#398—892no—
116#396—892no—
117#395—892no—
118#393—891no—
119#381—891no—
120#380—892no—
121C22×Q8—891no—
122C23×C4—891no—
123C2×C4⋊C4—892no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4C2×D8912yes—
129C2×C4⋊C4C2×D8911yescharacteristic
130C2×C22⋊C4—892no—
131C2×C22⋊C4—891no—
132C2×C22⋊C4C2×D8912yes—
133C2×C22⋊C4C2×D8911yescharacteristic
134#95—892no—
135#95—892no—
136#95—892no—
137#95—892no—
138#95—891no—
139#95—892no—
140#95—892no—
141#95C2×D8911yescharacteristic
142C24C22×D8911yescharacteristic
143C2×Q8—3561no—
144C2×Q8—3562no—
145C22×C4—894no—
146C22×C4—892no—
147C22×C4—892no—
148C22×C4—892no—
149C22×C4—892no—
150C22×C4—3561no—
151C22×C4—3561no—
152C22×C4C22×D8911yescharacteristic
153C22×C4C22×D8911yescharacteristic
154C22×C4C22×D8912yes—
155C22×C4C22×D8912yes—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—3562no—
159C4⋊C4—3562no—
160C4⋊C4—3562no—
161C4⋊C4—3562no—
162C4⋊C4—3562no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—3562no—
166C22⋊C4—3561no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D8912yes—
172C23C23×D8911yescharacteristic
173Q8—3564no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—894no—
185C2×C4—3564no—
186C2×C4—1782no—
187C2×C4—1782no—
188C2×C4—1782no—
189C2×C4—1782no—
190C2×C4—1782no—
191C2×C4—1782no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C2×Q8×D8911yescharacteristic
203C22#1566805711yescharacteristic
204C22#1566805712yes—
205C22#1566805811yescharacteristic
206C22#1566805912yes—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—3562no—
212C4—3562no—
213C4—3562no—
214C4—1784no—
215C2—42no—
216C2#1915222311yescharacteristic
217C2#1915222712yes—
218C2#1915233511yescharacteristic
219C2#1915234512yes—
220C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#399×C89C2
prime radicalC24×C89C23
hypercenter#399D89
hypocenterC89#2841
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #19151539C2semidirect
2. #19151531C2semidirect
3. #19151528C2semidirect
5. #19151518C2semidirect
35. C22×Dic89Q8semidirect
111. C89#2841semidirect

Maximal subgroups

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

subgroupindex
#191515392
#191515312
#191515282
#191515212
#191515182
#191515102
#191514592
#191514562
#399×C892
#284189