Finite Group Databasebeta

← #26026066

Subgroups — #26026066

Order 11392.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#15667992C211yesmaximal, characteristic
2C2×C4⋊C4×D89C211yesmaximal, characteristic
3#19151536C211yesmaximal, characteristic, complemented
4#19151532C212yesmaximal, complemented
5#19151530C212yesmaximal, complemented
6#19151519C211yesmaximal, characteristic, complemented
7#19151518C211yesmaximal, characteristic, complemented
8#19151472C212yesmaximal
9#19151460C212yesmaximal
10#19151457C211yesmaximal, characteristic
11#400×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15C22×C4×D89C2211yescharacteristic
16#15667992—24no—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2212yes—
19C2×C4⋊Dic89C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2212yes—
23C2×#13083553C2212yes—
24C4⋊C4×D89—24no—
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27#15667919C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C2×Dic178—22no—
39C2×Dic178—42no—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2312yes—
42C22×Dic89C2312yes—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C2×C4×D89—22no—
46C2×C4×D89—22no—
47C2×C4×D89—22no—
48C2×C4×D89—42no—
49C2×C4×D89—42no—
50C2×C4×D89D414yes—
51C2×C4×D89Q814yescomplemented
52C4⋊Dic89—24no—
53C4⋊Dic89—22no—
54C4⋊Dic89—42no—
55#13083553—22no—
56#13083553—22no—
57#13083553—42no—
58#13083553—42no—
59#13083551—24no—
60#13083551—24no—
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2312yes—
63C22×C4×C89C2312yes—
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C4⋊C4×C89—22no—
67C4⋊C4×C89—22no—
68C23×C89C2411yescharacteristic
69C22×D89—22no—
70C22×D89—22no—
71C22×D89C2×D412yes—
72C22×D89C2×Q812yes—
73C22×D89#4112yes—
74C2×C4×C89—21no—
75C2×C4×C89—21no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—24no—
83C2×C4×C89—22no—
84C2×C4×C89C2×D412yes—
85C2×C4×C89C2×Q812yes—
86C2×Dic89—21no—
87C2×Dic89—21no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—21no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89C2×D412yes—
98C2×Dic89C2×Q812yes—
99C4×D89—28no—
100C4×D89—44no—
101C4×D89—44no—
102Dic178—44no—
103C22×C89C22×D411yescharacteristic
104C22×C89C22×Q811yescharacteristic
105C22×C89C2×#4111yescharacteristic
106C22×C89H(5,𝔽2)12yes—
107C22×C892−1+412yes—
108C2×D89—22no—
109C2×D89—22no—
110C2×D89—24no—
111C2×D89—24no—
112C2×D89C22⋊Q814yes—
113C4×C89—22no—
114C4×C89—22no—
115C4×C89—41no—
116C4×C89—42no—
117C4×C89—42no—
118Dic89—22no—
119Dic89—22no—
120Dic89—42no—
121Dic89—41no—
122Dic89—42no—
123C2×C89C2×C22⋊Q811yescharacteristic
124C2×C89#53411yescharacteristic
125C2×C89#53611yescharacteristic
126C2×C89#53912yes—
127C2×C89#54412yes—
128D89—24no—
129#2627—891nomaximal, Sylow
130C89#262711yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—891no—
132C22×C4⋊C4—891no—
133#400—891no—
134#400D8911yescharacteristic, complemented
135#398—892no—
136#398—892no—
137#395—891no—
138#395—891no—
139#385—892no—
140#381—892no—
141#380—891no—
142C22×Q8—891no—
143C23×C4—891no—
144C23×C4—891no—
145C23×C4—891no—
146C22⋊Q8—1784no—
147C2×C4⋊C4—892no—
148C2×C4⋊C4—892no—
149C2×C4⋊C4—892no—
150C2×C4⋊C4—891no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—892no—
154C2×C4⋊C4—1784no—
155C2×C4⋊C4C2×D8911yescharacteristic
156C2×C4⋊C4C2×D8911yescharacteristic
157C2×C22⋊C4—892no—
158C2×C22⋊C4—892no—
159#95—891no—
160#95—892no—
161#95—892no—
162#95—892no—
163#95—892no—
164#95C2×D8911yescharacteristic
165#95C2×D8912yes—
166#95C2×D8912yes—
167C24—891no—
168C2×Q8—3562no—
169C2×Q8—1782no—
170C22×C4—891no—
171C22×C4—891no—
172C22×C4—894no—
173C22×C4—894no—
174C22×C4—892no—
175C22×C4—892no—
176C22×C4—891no—
177C22×C4—3562no—
178C22×C4—3562no—
179C22×C4—1782no—
180C22×C4—1782no—
181C22×C4—1782no—
182C22×C4C22×D8912yes—
183C22×C4C22×D8912yes—
184C22×C4C22×D8911yescharacteristic
185C22×C4C22×D8911yescharacteristic
186C22×C4C22×D8911yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—3562no—
190C4⋊C4—3562no—
191C4⋊C4—3562no—
192C4⋊C4—1782no—
193C4⋊C4—1782no—
194C4⋊C4—1784no—
195C4⋊C4—1782no—
196C22⋊C4—1784no—
197C22⋊C4—1784no—
198C23—892no—
199C23—892no—
200C23—892no—
201C23—1782no—
202C23—1782no—
203C23C23×D8911yescharacteristic
204Q8—3564no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—892no—
216C2×C4—892no—
217C2×C4—3564no—
218C2×C4—3564no—
219C2×C4—1788no—
220C2×C4—1782no—
221C2×C4—1781no—
222C2×C4—1782no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4—1782no—
228C2×C4—1781no—
229C2×C4—1781no—
230C2×C4—1782no—
231C2×C4D4×D8912yes—
232C2×C4Q8×D8912yes—
233C22—894no—
234C22—1782no—
235C22—1782no—
236C22—1784no—
237C22—1784no—
238C22C2×D4×D8911yescharacteristic
239C22C2×Q8×D8911yescharacteristic
240C22#41×D8911yescharacteristic
241C22#1566805812yes—
242C22#1566805912yes—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—3561no—
249C4—3562no—
250C4—3562no—
251C4—1782no—
252C4—1782no—
253C2—1784no—
254C2C22⋊Q8×D8911yescharacteristic
255C2#1915215911yescharacteristic
256C2#1915216811yescharacteristic
257C2#1915218912yes—
258C2#1915222812yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC23×D89C23
hypercenter#400D89
hypocenterC89#2627
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #19151536C2semidirect
4. #19151532C2semidirect
5. #19151530C2semidirect
6. #19151519C2semidirect
7. #19151518C2semidirect
11. #400×C89C2semidirect
51. C2×C4×D89Q8semidirect
130. C89#2627semidirect
134. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679922
C2×C4⋊C4×D892
#191515362
#191515322
#191515302
#191515192
#191515182
#191514722
#191514602
#191514572
#400×C892
#262789