Finite Group Databasebeta

← #26027281

Subgroups — #26027281

Order 11392.

456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668011C212yesmaximal
2#19151528C211yesmaximal, characteristic
3#19151519C212yesmaximal
4#19151518C212yesmaximal
5#19151503C211yesmaximal, characteristic
6#19151493C212yesmaximal
7#19151485C212yesmaximal
8#19151480C212yesmaximal
9#398×C89C211yesmaximal, characteristic
10C22×Dic178C2212yes—
11C22×Dic178C2211yescharacteristic
12#15668011—28no—
13C2×C4⋊Dic89C2212yes—
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×C4×Dic89C2212yes—
20C2×C4×Dic89C2211yescharacteristic
21#15667919C2211yescharacteristic
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2212yes—
27C2×C4⋊C4×C89C2212yes—
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#95×C89C2212yes—
31#95×C89C2211yescharacteristic
32C2×Dic178—24no—
33C2×Dic178—41no—
34C2×Dic178—41no—
35C2×Dic178—42no—
36C2×Dic178—42no—
37C2×Dic178D414yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C4⋊Dic89—24no—
43C4⋊Dic89—41no—
44#13083553—24no—
45#13083553—24no—
46#13083553—42no—
47#13083553Q818yescomplemented
48C4×Dic89—24no—
49C4×Dic89—41no—
50C22×C4×C89C2312yes—
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2311yescharacteristic
53C22×C4×C89C2311yescharacteristic
54C22×C4×C89C2312yes—
55C4⋊C4×C89—24no—
56C4⋊C4×C89—41no—
57C4⋊C4×C89—41no—
58C23×C89C2411yescharacteristic
59C2×C4×C89—22no—
60C2×C4×C89—21no—
61C2×C4×C89—21no—
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×C4×C89C2×D412yes—
71C2×C4×C89C2×Q814yes—
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×Dic89C2×D414yes—
82C2×Dic89C2×Q814yes—
83C2×Dic89C2×Q814yes—
84Dic178—44no—
85Dic178—48no—
86C22×C89C22×D411yescharacteristic
87C22×C89C22×Q812yes—
88C22×C89H(5,𝔽2)11yescharacteristic
89C22×C89H(5,𝔽2)11yescharacteristic
90C22×C892−1+412yes—
91C4×C89—22no—
92C4×C89—24no—
93C4×C89—42no—
94C4×C89—41no—
95C4×C89—41no—
96Dic89—24no—
97Dic89—24no—
98Dic89—24no—
99Dic89—42no—
100C2×C89#53411yescharacteristic
101C2×C89#54412yes—
102C2×C89D4×Q812yes—
103C2×C89Q8211yescharacteristic
104C2×C89#56311yescharacteristic
105#2734—891nomaximal, Sylow
106C89#273411yescharacteristic, complemented, Sylow
107C2×C4⋊Q8—892no—
108#398—891no—
109#398D8911yescharacteristic
110#395—892no—
111#395—892no—
112#391—891no—
113#389—892no—
114#387—892no—
115#387—892no—
116C22×Q8—891no—
117C22×Q8—892no—
118C4⋊Q8—1788no—
119C2×C4⋊C4—892no—
120C2×C4⋊C4—892no—
121C2×C4⋊C4—891no—
122C2×C4⋊C4—892no—
123C2×C4⋊C4—892no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4C2×D8912yes—
126C2×C4⋊C4C2×D8911yescharacteristic
127C2×C4⋊C4C2×D8911yescharacteristic
128C2×C42—891no—
129C2×C42—892no—
130#95—891no—
131#95—892no—
132#95—892no—
133#95—892no—
134#95—892no—
135#95—892no—
136#95C2×D8911yescharacteristic
137#95C2×D8912yes—
138C2×Q8—894no—
139C2×Q8—3561no—
140C2×Q8—3561no—
141C2×Q8—3562no—
142C2×Q8—3562no—
143C2×Q8—1784no—
144C22×C4—892no—
145C22×C4—892no—
146C22×C4—892no—
147C22×C4—892no—
148C22×C4C22×D8911yescharacteristic
149C22×C4C22×D8911yescharacteristic
150C22×C4C22×D8912yes—
151C22×C4C22×D8911yescharacteristic
152C22×C4C22×D8912yes—
153C4⋊C4—24no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—898no—
157C4⋊C4—3562no—
158C4⋊C4—3561no—
159C4⋊C4—1784no—
160C4⋊C4—1784no—
161C4⋊C4—1784no—
162C42—3561no—
163C42—1784no—
164C23C23×D8911yescharacteristic
165Q8—3564no—
166Q8—3568no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
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—894no—
180C2×C4—894no—
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×C4D4×D8912yes—
191C2×C4Q8×D8914yes—
192C22C2×D4×D8911yescharacteristic
193C22C2×Q8×D8912yes—
194C22#1566805711yescharacteristic
195C22#1566805811yescharacteristic
196C22#1566805912yes—
197C4—22no—
198C4—24no—
199C4—42no—
200C4—41no—
201C4—41no—
202C4—3562no—
203C4—1784no—
204C4—1784no—
205C4—1784no—
206C2#1915215611yescharacteristic
207C2#1915222812yes—
208C2#1915226112yes—
209C2#1915232811yescharacteristic
210C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#398×C89C2
hypercenter#398D89
hypocenterC89#2734
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
47. #13083553Q8semidirect
106. C89#2734semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
#191515282
#191515192
#191515182
#191515032
#191514932
#191514852
#191514802
#398×C892
#273489