Finite Group Databasebeta

← #26025263

Subgroups — #26025263

Order 11392.

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

normal subgroups only

This group has 544 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×#15667991C212yesmaximal
2#19151532C212yesmaximal, complemented
3#19151519C212yesmaximal, complemented
4#19151502C212yesmaximal, complemented
5#19151495C212yesmaximal, complemented
6#19151471C212yesmaximal
7#19151458C211yesmaximal, characteristic
8C4×C22⋊Dic89C211yesmaximal, characteristic
9C2×#95×C89C211yesmaximal, characteristic
10C22×Dic178C2212yes—
11#15667991—28no—
12C2×C4⋊Dic89C2212yes—
13C2×C4⋊Dic89C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×C22⋊Dic89C2212yes—
19C2×C22⋊Dic89C2211yescharacteristic
20C2×C22⋊Dic89C2211yescharacteristic
21C2×C4×Dic89C2212yes—
22#15667919C2212yes—
23#15667919C2211yescharacteristic
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2212yes—
27C23×C4×C89C2212yes—
28C23×C4×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31#95×C89C2211yescharacteristic
32C2×Dic178—24no—
33C2×Dic178—24no—
34C2×Dic178—42no—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C4⋊Dic89—24no—
40C4⋊Dic89—42no—
41#13083553—24no—
42#13083553—24no—
43#13083553—24no—
44#13083553—42no—
45C22⋊Dic89—24no—
46C22⋊Dic89D414yes—
47C22⋊Dic89Q814yescomplemented
48C4×Dic89—42no—
49C24×C89C2311yescharacteristic
50C22×C4×C89—24no—
51C22×C4×C89—24no—
52C22×C4×C89—42no—
53C22×C4×C89—42no—
54C22×C4×C89Q814yescomplemented
55C22×C4×C89C2312yes—
56C22×C4×C89C2311yescharacteristic
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2312yes—
59C23×C89—22no—
60C23×C89—22no—
61C23×C89C2×D412yes—
62C23×C89C2×Q812yes—
63C23×C89C2×Q812yes—
64C23×C89C2411yescharacteristic
65C2×C4×C89—22no—
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×C4×C89—44no—
73C2×C4×C89—48no—
74C2×C4×C89C2×Q812yes—
75C2×C4×C89C2×Q812yes—
76C2×C4×C89#4114yes—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89C2×D414yes—
88C2×Dic89C2×Q814yes—
89Dic178—48no—
90C22×C89—22no—
91C22×C89—22no—
92C22×C89—24no—
93C22×C89—24no—
94C22×C89C4⋊Q814yes—
95C22×C89C22×D411yescharacteristic
96C22×C89C22×Q811yescharacteristic
97C22×C89C22×Q811yescharacteristic
98C22×C89C2×#4112yes—
99C22×C89H(5,𝔽2)12yes—
100C4×C89—22no—
101C4×C89—22no—
102C4×C89—24no—
103C4×C89—42no—
104Dic89—24no—
105Dic89—24no—
106Dic89—42no—
107Dic89—42no—
108C2×C89—24no—
109C2×C89C2×C4⋊Q811yescharacteristic
110C2×C89#53311yescharacteristic
111C2×C89#54311yescharacteristic
112C2×C89#54612yes—
113C2×C89#55412yes—
114#2549—891nomaximal, Sylow
115C89#254911yescharacteristic, complemented, Sylow
116C2×C22⋊Q8—892no—
117#398—892no—
118#395—892no—
119#391—892no—
120#389—892no—
121#385—892no—
122#380—891no—
123C4×C22⋊C4—891no—
124C2×#95D8911yescharacteristic
125C22×Q8—892no—
126C23×C4C2×D8912yes—
127C23×C4C2×D8911yescharacteristic
128C22⋊Q8—1788no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4—892no—
131C2×C4⋊C4—892no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—892no—
134C2×C4⋊C4—892no—
135C2×C22⋊C4—891no—
136C2×C22⋊C4—891no—
137C2×C22⋊C4—892no—
138C2×C42—892no—
139#95—892no—
140#95—891no—
141#95—891no—
142#95—892no—
143#95—892no—
144#95C2×D8912yes—
145#95C2×D8911yescharacteristic
146#95C2×D8911yescharacteristic
147C24C22×D8911yescharacteristic
148C2×Q8—3562no—
149C2×Q8—1784no—
150C2×Q8—1784no—
151C22×C4—24no—
152C22×C4—24no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—892no—
156C22×C4—892no—
157C22×C4—892no—
158C22×C4—892no—
159C22×C4Dic17814yescomplemented
160C22×C4C22×D8912yes—
161C22×C4C22×D8911yescharacteristic
162C22×C4C22×D8911yescharacteristic
163C22×C4C22×D8912yes—
164C4⋊C4—3562no—
165C4⋊C4—3562no—
166C4⋊C4—1784no—
167C4⋊C4—1784no—
168C4⋊C4—1784no—
169C4⋊C4—1784no—
170C22⋊C4—894no—
171C22⋊C4—894no—
172C22⋊C4—1784no—
173C42—3562no—
174C23—22no—
175C23—22no—
176C23D4×D8912yes—
177C23Q8×D8912yes—
178C23C2×Dic17812yes—
179C23C23×D8911yescharacteristic
180Q8—3568no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—44no—
189C2×C4—48no—
190C2×C4—894no—
191C2×C4—894no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4C2×Dic17812yes—
203C2×C4C2×Dic17812yes—
204C2×C4#1308357414yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22#1566801114yes—
210C22C2×D4×D8911yescharacteristic
211C22C2×Q8×D8911yescharacteristic
212C22C22×Dic17811yescharacteristic
213C22C2×#1308357412yes—
214C22#1566805712yes—
215C4—22no—
216C4—22no—
217C4—24no—
218C4—42no—
219C4—3562no—
220C4—3562no—
221C4—1784no—
222C4—1784no—
223C2—24no—
224C2C2×#1566801111yescharacteristic
225C2#1915215511yescharacteristic
226C2#1915222411yescharacteristic
227C2#1915223812yes—
228C2#1915230312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
FittingC2×#95×C89C2
prime radicalC24×C89C23
hypercenterC2×#95D89
hypocenterC89#2549
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #19151532C2semidirect
3. #19151519C2semidirect
4. #19151502C2semidirect
5. #19151495C2semidirect
47. C22⋊Dic89Q8semidirect
54. C22×C4×C89Q8semidirect
115. C89#2549semidirect
159. C22×C4Dic178semidirect

Maximal subgroups

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

subgroupindex
C2×#156679912
#191515322
#191515192
#191515022
#191514952
#191514712
#191514582
C4×C22⋊Dic892
C2×#95×C892
#254989