Finite Group Databasebeta

← #26027179

Subgroups — #26027179

Order 11392.

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

normal subgroups only

This group has 504 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
1C2×#15667997C212yesmaximal
2#19151528C211yesmaximal, characteristic, complemented
3#19151527C212yesmaximal, complemented
4#19151527C212yesmaximal, complemented
5#19151499C211yesmaximal, characteristic
6#19151493C212yesmaximal, complemented
7#19151472C212yesmaximal, complemented
8#19151469C212yesmaximal, complemented
9#398×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C22×C4×D89C2212yes—
12#15667997—28no—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×C4×Dic89C2211yescharacteristic
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2211yescharacteristic
27C2×C4⋊C4×C89C2212yes—
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#95×C89C2212yes—
31#95×C89C2211yescharacteristic
32C23×D89C2312yes—
33C2×D356—41no—
34C2×D356—41no—
35C2×D356D414yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C2×C4×D89—24no—
40C2×C4×D89—42no—
41C2×C4×D89—42no—
42C4⋊Dic89—41no—
43#13083553—24no—
44#13083553—24no—
45#13083553—42no—
46#13083551—24no—
47#13083551—24no—
48#13083551—24no—
49#13083551—24no—
50#13083551—24no—
51C4×Dic89—41no—
52C22×C4×C89C2312yes—
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2311yescharacteristic
57C4⋊C4×C89—24no—
58C4⋊C4×C89—41no—
59C4⋊C4×C89—41no—
60C23×C89C2411yescharacteristic
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—22no—
65C22×D89—22no—
66C22×D89—22no—
67C22×D89C2×D414yes—
68C2×C4×C89—21no—
69C2×C4×C89—21no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—21no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89C2×D412yes—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89#4114yes—
90D356—44no—
91C4×D89—48no—
92C22×C89C22×D411yescharacteristic
93C22×C89C2×#4112yes—
94C22×C89H(5,𝔽2)11yescharacteristic
95C22×C89H(5,𝔽2)11yescharacteristic
96C22×C892−1+412yes—
97C2×D89—24no—
98C2×D89—24no—
99C2×D89—24no—
100C2×D89—42no—
101C2×D89—42no—
102C2×D89—42no—
103C2×D89—42no—
104C4×C89—22no—
105C4×C89—42no—
106C4×C89—42no—
107C4×C89—41no—
108C4×C89—41no—
109Dic89—24no—
110Dic89—42no—
111Dic89—42no—
112C2×C89#53411yescharacteristic
113C2×C89#53912yes—
114C2×C89#54712yes—
115C2×C89#55911yescharacteristic
116C2×C89#56311yescharacteristic
117D89—44no—
118#2724—891nomaximal, Sylow
119C89#272411yescharacteristic, complemented, Sylow
120C2×#123—892no—
121#398—891no—
122#398D8911yescharacteristic, complemented
123#397—892no—
124#397—892no—
125#390—891no—
126#389—892no—
127#385—892no—
128#385—892no—
129C22×D4—891no—
130C23×C4—892no—
131#123—1788no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—891no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4—892no—
136C2×C4⋊C4C2×D8912yes—
137C2×C4⋊C4C2×D8911yescharacteristic
138C2×C4⋊C4C2×D8911yescharacteristic
139C2×C22⋊C4—892no—
140C2×C22⋊C4—892no—
141C2×C22⋊C4—892no—
142C2×C22⋊C4—892no—
143C2×C22⋊C4—892no—
144C2×C42—891no—
145#95—892no—
146#95—892no—
147#95—892no—
148#95—891no—
149#95C2×D8912yes—
150#95C2×D8911yescharacteristic
151C24—892no—
152C2×D4—894no—
153C2×D4—3561no—
154C2×D4—3561no—
155C22×C4—892no—
156C22×C4—892no—
157C22×C4—892no—
158C22×C4—3562no—
159C22×C4—3562no—
160C22×C4—1784no—
161C22×C4C22×D8911yescharacteristic
162C22×C4C22×D8912yes—
163C22×C4C22×D8911yescharacteristic
164C22×C4C22×D8912yes—
165C22×C4C22×D8911yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—3562no—
170C4⋊C4—3561no—
171C4⋊C4—1784no—
172C4⋊C4—1784no—
173C22⋊C4—1784no—
174C22⋊C4—1784no—
175C22⋊C4—1784no—
176C22⋊C4—1784no—
177C22⋊C4—1784no—
178C42—3561no—
179C23—894no—
180C23—1782no—
181C23—1782no—
182C23—1782no—
183C23—1782no—
184C23—1782no—
185C23—1782no—
186C23C23×D8911yescharacteristic
187D4—3564no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—894no—
201C2×C4—3568no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4D4×D8912yes—
211C22—3562no—
212C22—3562no—
213C22—3562no—
214C22—3562no—
215C22—1784no—
216C22—1784no—
217C22—1784no—
218C22C2×D4×D8911yescharacteristic
219C22#41×D8912yes—
220C22#1566805711yescharacteristic
221C22#1566805811yescharacteristic
222C22#1566806012yes—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—3562no—
229C4—3562no—
230C4—1784no—
231C2—3564no—
232C2#1915215611yescharacteristic
233C2#1915219612yes—
234C2#1915225012yes—
235C2#1915233211yescharacteristic
236C2#1915234711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2724
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #19151528C2semidirect
3. #19151527C2semidirect
4. #19151527C2semidirect
6. #19151493C2semidirect
7. #19151472C2semidirect
8. #19151469C2semidirect
9. #398×C89C2semidirect
119. C89#2724semidirect
122. #398D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679972
#191515282
#191515272
#191514992
#191514932
#191514722
#191514692
#398×C892
#272489