Finite Group Databasebeta

← #26027375

Subgroups — #26027375

Order 11392.

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

normal subgroups only

This group has 416 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#19151539C212yesmaximal, complemented
2#19151534C211yesmaximal, characteristic
3#19151517C212yesmaximal, complemented
4#19151495C212yesmaximal, complemented
5#19151486C212yesmaximal
6#19151480C212yesmaximal, complemented
7#19151470C211yesmaximal, characteristic
8#19151456C212yesmaximal
9#393×C89C211yesmaximal, characteristic
10C23×Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×#13083553C2212yes—
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×C22⋊Dic89C2212yes—
18C2×C22⋊Dic89C2211yescharacteristic
19C2×C4×Dic89C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26C22×Q8×C89C2211yescharacteristic
27C2×C22⋊C4×C89C2212yes—
28C2×C22⋊C4×C89C2211yescharacteristic
29#95×C89C2211yescharacteristic
30#95×C89C2212yes—
31C22×Dic89—24no—
32C22×Dic89—41no—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C4⋊Dic89—41no—
38#13083553—24no—
39#13083553—24no—
40#13083553—42no—
41#13083553—42no—
42#13083553—42no—
43C22⋊Dic89—42no—
44C22⋊Dic89Q814yescomplemented
45C4×Dic89—42no—
46C24×C89C2311yescharacteristic
47C2×Q8×C89—42no—
48C2×Q8×C89—41no—
49C22×C4×C89C2312yes—
50C22×C4×C89C2311yescharacteristic
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22⋊C4×C89—42no—
54C22⋊C4×C89—41no—
55C23×C89—22no—
56C23×C89—22no—
57C23×C89—21no—
58C23×C89—21no—
59C23×C89C2×Q812yes—
60C23×C89C2411yescharacteristic
61Q8×C89—44no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
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—44no—
83C2×Dic89C2×Q814yes—
84C2×Dic89#4114yes—
85C22×C89—22no—
86C22×C89—24no—
87C22×C89—42no—
88C22×C89—41no—
89C22×C89—41no—
90C22×C89C22×Q811yescharacteristic
91C22×C89C2×#4112yes—
92C22×C89H(5,𝔽2)12yes—
93C22×C89H(5,𝔽2)11yescharacteristic
94C22×C892−1+411yescharacteristic
95C4×C89—42no—
96C4×C89—41no—
97C4×C89—42no—
98C4×C89—41no—
99Dic89—24no—
100Dic89—24no—
101Dic89—42no—
102Dic89—42no—
103C2×C89—42no—
104C2×C89#54212yes—
105C2×C89#54411yescharacteristic
106C2×C89#55111yescharacteristic
107C2×C89#55412yes—
108C2×C89#56011yescharacteristic
109#2742—891nomaximal, Sylow
110C89#274211yescharacteristic, complemented, Sylow
111#400—892no—
112#399—891no—
113#395—892no—
114#393D8911yescharacteristic
115#389—892no—
116#388—892no—
117#387—892no—
118#385—891no—
119#380—892no—
120C22×Q8C2×D8911yescharacteristic
121C23×C4—891no—
122C2×C4⋊C4—892no—
123C2×C4⋊C4—892no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4—891no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C22⋊C4—891no—
129C2×C22⋊C4—892no—
130C2×C22⋊C4C2×D8912yes—
131C2×C22⋊C4C2×D8911yescharacteristic
132C2×C42—892no—
133#95—892no—
134#95—892no—
135#95—892no—
136#95—892no—
137#95—892no—
138#95—891no—
139#95C2×D8911yescharacteristic
140#95C2×D8912yes—
141C24C22×D8911yescharacteristic
142C2×Q8—42no—
143C2×Q8—41no—
144C22×C4—892no—
145C22×C4—892no—
146C22×C4—892no—
147C22×C4—892no—
148C22×C4—3561no—
149C22×C4—1784no—
150C22×C4C22×D8912yes—
151C22×C4C22×D8912yes—
152C22×C4C22×D8911yescharacteristic
153C22×C4C22×D8911yescharacteristic
154C4⋊C4—3562no—
155C4⋊C4—3562no—
156C4⋊C4—3562no—
157C4⋊C4—3561no—
158C4⋊C4—1784no—
159C4⋊C4—1784no—
160C22⋊C4—42no—
161C22⋊C4—41no—
162C22⋊C4—894no—
163C22⋊C4—3562no—
164C42—3562no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23—21no—
169C23Q8×D8912yes—
170C23C23×D8911yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
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—894no—
183C2×C4—894no—
184C2×C4—3564no—
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—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C2×Q8×D8911yescharacteristic
201C22#41×D8912yes—
202C22#1566805712yes—
203C22#1566805711yescharacteristic
204C22#1566805911yescharacteristic
205C4—42no—
206C4—41no—
207C4—42no—
208C4—41no—
209C4—3562no—
210C4—3562no—
211C4—1784no—
212C4—1784no—
213C2—42no—
214C2#1915221212yes—
215C2#1915222711yescharacteristic
216C2#1915227811yescharacteristic
217C2#1915230212yes—
218C2#1915233711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#393×C89C2
prime radicalC24×C89C23
hypercenter#393D89
hypocenterC89#2742
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #19151539C2semidirect
3. #19151517C2semidirect
4. #19151495C2semidirect
6. #19151480C2semidirect
44. C22⋊Dic89Q8semidirect
110. C89#2742semidirect

Maximal subgroups

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

subgroupindex
#191515392
#191515342
#191515172
#191514952
#191514862
#191514802
#191514702
#191514562
#393×C892
#274289