Finite Group Databasebeta

← #26023420

Subgroups — #26023420

Order 11392.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15667991C211yesmaximal, characteristic
2#19151502C212yesmaximal, complemented
3#19151495C212yesmaximal, complemented
4#19151492C212yesmaximal
5#19151486C212yesmaximal
6#19151485C212yesmaximal, complemented
7#19151483C212yesmaximal, complemented
8#19151458C211yesmaximal, characteristic
9#381×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11#15667991C418yescomplemented
12C2×C4⋊Dic89C2212yes—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×C22⋊Dic89C2211yescharacteristic
18C2×C22⋊Dic89C2211yescharacteristic
19C2×C22⋊Dic89C2212yes—
20C2×C4×Dic89C2212yes—
21C2×C4×Dic89C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2212yes—
27C23×C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89C2212yes—
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31#95×C89C2211yescharacteristic
32C2×Dic178—42no—
33C2×Dic178C2×C414yes—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C4⋊Dic89—42no—
39C4⋊Dic89C2×C414yes—
40#13083553—42no—
41#13083553—42no—
42#13083553C2×C418yes—
43C22⋊Dic89—41no—
44C22⋊Dic89—41no—
45C22⋊Dic89C2×C418yes—
46C4×Dic89—42no—
47C4×Dic89—42no—
48C24×C89C2311yescharacteristic
49C22×C4×C89—42no—
50C22×C4×C89C2×C414yes—
51C22×C4×C89C2312yes—
52C22×C4×C89C2312yes—
53C22×C4×C89C2311yescharacteristic
54C22×C4×C89C2311yescharacteristic
55C22⋊C4×C89—42no—
56C23×C89—22no—
57C23×C89—21no—
58C23×C89—22no—
59C23×C89—21no—
60C23×C89C22×C412yes—
61C23×C89C2411yescharacteristic
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—44no—
71C2×C4×C89C22×C412yes—
72C2×C4×C89C22×C412yes—
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×Dic89C22×C414yes—
84C2×Dic89C22×C414yes—
85Dic178—44no—
86C22×C89—22no—
87C22×C89—22no—
88C22×C89—22no—
89C22×C89—42no—
90C22×C89—42no—
91C22×C89C23×C411yescharacteristic
92C22×C89H(5,𝔽2)12yes—
93C22×C89H(5,𝔽2)11yescharacteristic
94C22×C892−1+412yes—
95C22×C892−1+411yescharacteristic
96C4×C89—22no—
97C4×C89—22no—
98C4×C89—42no—
99C4×C89—42no—
100Dic89—24no—
101Dic89—24no—
102Dic89—42no—
103Dic89—42no—
104C2×C89—42no—
105C2×C89#51811yescharacteristic
106C2×C89#51911yescharacteristic
107C2×C89#52011yescharacteristic
108C2×C89#56212yes—
109C2×C89#56312yes—
110#2378—891nomaximal, Sylow
111C89#237811yescharacteristic, complemented, Sylow
112C2×C22⋊Q8—891no—
113#391—892no—
114#389—892no—
115#388—892no—
116#388—892no—
117#387—892no—
118#387—892no—
119#381D8911yescharacteristic
120#380—891no—
121C22×Q8—891no—
122C23×C4C2×D8911yescharacteristic
123C22⋊Q8—898no—
124C2×C4⋊C4—891no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—892no—
129C2×C22⋊C4—892no—
130C2×C22⋊C4—891no—
131C2×C22⋊C4—891no—
132C2×C22⋊C4C2×D8912yes—
133C2×C42—892no—
134C2×C42—892no—
135#95—892no—
136#95—892no—
137#95—892no—
138#95—892no—
139#95—892no—
140#95C2×D8911yescharacteristic
141#95C2×D8912yes—
142#95C2×D8911yescharacteristic
143C24C22×D8911yescharacteristic
144C2×Q8—894no—
145C2×Q8—3562no—
146C22×C4—42no—
147C22×C4—892no—
148C22×C4—892no—
149C22×C4—892no—
150C22×C4—892no—
151C22×C4C4×D8914yes—
152C22×C4C22×D8912yes—
153C22×C4C22×D8912yes—
154C22×C4C22×D8911yescharacteristic
155C22×C4C22×D8911yescharacteristic
156C4⋊C4—898no—
157C4⋊C4—894no—
158C4⋊C4—3562no—
159C4⋊C4—3562no—
160C4⋊C4—3562no—
161C22⋊C4—42no—
162C22⋊C4—898no—
163C22⋊C4—3561no—
164C22⋊C4—3561no—
165C42—3562no—
166C42—3562no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D8912yes—
172C23C23×D8911yescharacteristic
173Q8—3564no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—894no—
184C2×C4—894no—
185C2×C4—1782no—
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×C4C2×C4×D8912yes—
196C2×C4C2×C4×D8912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D8911yescharacteristic
203C22#1566805712yes—
204C22#1566805811yescharacteristic
205C22#1566805912yes—
206C22#1566805911yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—3562no—
212C4—3562no—
213C4—1784no—
214C4—1784no—
215C2—42no—
216C2#1915207111yescharacteristic
217C2#1915207511yescharacteristic
218C2#1915207811yescharacteristic
219C2#1915234512yes—
220C2#1915235112yes—
subgroupG/H
center, FrattiniC23C23×D89
commutatorC22×C89C23×C4
Fitting#381×C89C2
socle, cosocleC23×C89C24
prime radicalC24×C89C23
hypercenter#381D89
hypocenterC89#2378
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #19151502C2semidirect
3. #19151495C2semidirect
6. #19151485C2semidirect
7. #19151483C2semidirect
11. #15667991C4semidirect
111. C89#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#156679912
#191515022
#191514952
#191514922
#191514862
#191514852
#191514832
#191514582
#381×C892
#237889