Finite Group Databasebeta

← #26027771

Subgroups — #26027771

Order 11392.

392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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#19151540C212yesmaximal, complemented
2#19151540C212yesmaximal, complemented
3#19151534C211yesmaximal, characteristic
4#19151493C212yesmaximal, complemented
5#19151491C212yesmaximal
6#19151483C212yesmaximal, complemented
7#19151470C212yesmaximal
8#19151459C211yesmaximal, characteristic
9#397×C89C211yesmaximal, characteristic
10C23×Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2212yes—
12C2×C4⋊Dic89C2211yescharacteristic
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C22⋊Dic89C2212yes—
17C2×C22⋊Dic89C2211yescharacteristic
18C2×C4×Dic89C2212yes—
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2212yes—
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C22⋊C4×C89C2212yes—
28C2×C22⋊C4×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31C22×Dic89—22no—
32C22×Dic89—41no—
33C22×Dic89—41no—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C4⋊Dic89—24no—
39C4⋊Dic89—41no—
40#13083553—24no—
41#13083553—42no—
42#13083553—42no—
43C22⋊Dic89—24no—
44C22⋊Dic89—41no—
45C4×Dic89—42no—
46C24×C89C2311yescharacteristic
47C22×C4×C89C2312yes—
48C22×C4×C89C2311yescharacteristic
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C4⋊C4×C89—41no—
52C22⋊C4×C89—24no—
53C22⋊C4×C89—41no—
54C23×C89—22no—
55C23×C89—21no—
56C23×C89—21no—
57C23×C89—22no—
58C23×C89#4112yes—
59C23×C89C2411yescharacteristic
60C2×C4×C89—22no—
61C2×C4×C89—22no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—21no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×Dic89—22no—
71C2×Dic89—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—44no—
82C2×Dic89#4114yes—
83C22×C89—22no—
84C22×C89—24no—
85C22×C89—42no—
86C22×C89—41no—
87C22×C89—41no—
88C22×C89C2×#4111yescharacteristic
89C22×C89C2×#4112yes—
90C22×C89H(5,𝔽2)11yescharacteristic
91C22×C89H(5,𝔽2)11yescharacteristic
92C22×C892−1+412yes—
93C4×C89—42no—
94C4×C89—42no—
95C4×C89—41no—
96C4×C89—41no—
97Dic89—24no—
98Dic89—42no—
99Dic89—42no—
100Dic89—42no—
101C2×C89—42no—
102C2×C89#53811yescharacteristic
103C2×C89#53912yes—
104C2×C89#55212yes—
105C2×C89#55911yescharacteristic
106C2×C89#56311yescharacteristic
107#2771—891nomaximal, Sylow
108C89#277111yescharacteristic, complemented, Sylow
109#400—892no—
110#400—892no—
111#399—891no—
112#397D8911yescharacteristic
113#389—892no—
114#388—892no—
115#387—892no—
116#385—892no—
117#381—891no—
118C23×C4—891no—
119C2×C4⋊C4—892no—
120C2×C4⋊C4—892no—
121C2×C4⋊C4—891no—
122C2×C4⋊C4—892no—
123C2×C4⋊C4—892no—
124C2×C4⋊C4C2×D8911yescharacteristic
125C2×C22⋊C4—891no—
126C2×C22⋊C4—892no—
127C2×C22⋊C4C2×D8912yes—
128C2×C22⋊C4C2×D8911yescharacteristic
129C2×C42—892no—
130#95—892no—
131#95—892no—
132#95—892no—
133#95—892no—
134#95—891no—
135#95—892no—
136#95—892no—
137#95C2×D8912yes—
138#95C2×D8911yescharacteristic
139C24C22×D8911yescharacteristic
140C22×C4—892no—
141C22×C4—892no—
142C22×C4—892no—
143C22×C4—892no—
144C22×C4—3561no—
145C22×C4—3561no—
146C22×C4—1782no—
147C22×C4C22×D8912yes—
148C22×C4C22×D8911yescharacteristic
149C22×C4C22×D8911yescharacteristic
150C22×C4C22×D8912yes—
151C4⋊C4—41no—
152C4⋊C4—3562no—
153C4⋊C4—3562no—
154C4⋊C4—3561no—
155C4⋊C4—1784no—
156C4⋊C4—1784no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—3561no—
160C22⋊C4—1784no—
161C42—3562no—
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23#1308357312yes—
167C23C23×D8911yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—894no—
179C2×C4—3564no—
180C2×C4—1782no—
181C2×C4—1782no—
182C2×C4—1782no—
183C2×C4—1782no—
184C2×C4—1782no—
185C2×C4—1782no—
186C2×C4—1782no—
187C2×C4—1782no—
188C2×C4—1782no—
189C2×C4—1782no—
190C2×C4—1782no—
191C22—22no—
192C22—24no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22#41×D8912yes—
197C22C2×#1308357311yescharacteristic
198C22#1566805711yescharacteristic
199C22#1566805811yescharacteristic
200C22#1566805912yes—
201C4—42no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—3562no—
206C4—3562no—
207C4—3562no—
208C4—1784no—
209C2—42no—
210C2#1915218511yescharacteristic
211C2#1915218912yes—
212C2#1915228512yes—
213C2#1915233211yescharacteristic
214C2#1915234811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×C89C23
hypercenter#397D89
hypocenterC89#2771
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #19151540C2semidirect
2. #19151540C2semidirect
4. #19151493C2semidirect
6. #19151483C2semidirect
108. C89#2771semidirect

Maximal subgroups

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

subgroupindex
#191515402
#191515342
#191514932
#191514912
#191514832
#191514702
#191514592
#397×C892
#277189