Finite Group Databasebeta

← #26025414

Subgroups — #26025414

Order 11392.

532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15668002C211yesmaximal, characteristic, complemented
2C2×#15667974C211yesmaximal, characteristic
3#19151536C211yesmaximal, characteristic, complemented
4#19151516C211yesmaximal, characteristic
5#19151515C211yesmaximal, characteristic
6#19151490C212yesmaximal, complemented
7#19151487C212yesmaximal, complemented
8#19151457C212yesmaximal, complemented
9#19151457C212yesmaximal, complemented
10#19151449C211yesmaximal, characteristic, complemented
11#400×C89C211yesmaximal, characteristic, complemented
12C22×D356C2211yescharacteristic
13C22×C4×D89C2212yes—
14#15668002—24no—
15#15667974—24no—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27C2×C4×Dic89C2212yes—
28C2×C4×Dic89C2211yescharacteristic
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C23×D89C2312yes—
38C2×D356—24no—
39C2×D356—22no—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C2×C4×D89—24no—
46C2×C4×D89—24no—
47C2×C4×D89—24no—
48C4⋊Dic89—22no—
49#13083553—22no—
50#13083553—22no—
51#13083553—22no—
52#13083553—22no—
53#13083553—24no—
54#13083551—24no—
55#13083551—24no—
56#13083551—24no—
57#13083551—42no—
58#13083551—42no—
59C4×Dic89—42no—
60C4×Dic89D414yes—
61C22×C4×C89C2312yes—
62C22×C4×C89C2312yes—
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C4⋊C4×C89—22no—
67C4⋊C4×C89—22no—
68C23×C89C2411yescharacteristic
69C22×D89—22no—
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—22no—
73C22×D89—22no—
74C22×D89—22no—
75C22×D89#4114yes—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—21no—
87C2×C4×C89—21no—
88C2×C4×C89C2×D412yes—
89C2×Dic89—21no—
90C2×Dic89—21no—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—21no—
98C2×Dic89—21no—
99C2×Dic89C2×D412yes—
100C2×Dic89C2×D412yes—
101C2×Dic89#4114yes—
102D356—28no—
103C4×D89—48no—
104C22×C89C22×D411yescharacteristic
105C22×C89C2×#4112yes—
106C22×C89C2×#4112yes—
107C22×C89H(5,𝔽2)11yescharacteristic
108C22×C892−1+411yescharacteristic
109C2×D89—24no—
110C2×D89—24no—
111C2×D89—24no—
112C2×D89—42no—
113C2×D89—42no—
114C2×D89—42no—
115C2×D89—42no—
116C4×C89—22no—
117C4×C89—41no—
118C4×C89—42no—
119C4×C89—41no—
120C4×C89—42no—
121Dic89—22no—
122Dic89—41no—
123Dic89—41no—
124Dic89—42no—
125Dic89#12414yes—
126C2×C89#52511yescharacteristic
127C2×C89C2×#12411yescharacteristic
128C2×C89#53711yescharacteristic
129C2×C89#55212yes—
130C2×C89#55312yes—
131D89—44no—
132#2562—891nomaximal, Sylow
133C89#256211yescharacteristic, complemented, Sylow
134C2×#125—891no—
135C2×C4×D4—891no—
136#400—891no—
137#400D8911yescharacteristic, complemented
138#394—891no—
139#394—891no—
140#388—892no—
141#388—892no—
142#380—892no—
143#380—892no—
144C4×C4⋊C4—891no—
145C22×D4—891no—
146C23×C4—892no—
147#125—1784no—
148C4×D4—1784no—
149C2×C4⋊C4—891no—
150C2×C4⋊C4—891no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4—892no—
155C2×C4⋊C4C2×D8911yescharacteristic
156C2×C4⋊C4C2×D8911yescharacteristic
157C2×C22⋊C4—892no—
158C2×C22⋊C4—892no—
159C2×C22⋊C4—892no—
160C2×C22⋊C4—892no—
161C2×C22⋊C4—892no—
162C2×C42—891no—
163C2×C42—892no—
164#95—891no—
165#95—892no—
166#95—892no—
167#95C2×D8911yescharacteristic
168#95C2×D8912yes—
169#95C2×D8912yes—
170C24—892no—
171C2×D4—1784no—
172C2×D4—1782no—
173C22×C4—891no—
174C22×C4—891no—
175C22×C4—892no—
176C22×C4—891no—
177C22×C4—891no—
178C22×C4—1784no—
179C22×C4—1784no—
180C22×C4—1784no—
181C22×C4C22×D8912yes—
182C22×C4C22×D8912yes—
183C22×C4C22×D8911yescharacteristic
184C22×C4C22×D8911yescharacteristic
185C22×C4C22×D8911yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—1782no—
189C4⋊C4—1782no—
190C4⋊C4—1782no—
191C4⋊C4—1782no—
192C4⋊C4—1784no—
193C4⋊C4—1782no—
194C22⋊C4—3562no—
195C22⋊C4—3562no—
196C22⋊C4—1784no—
197C22⋊C4—1784no—
198C22⋊C4—1784no—
199C42—894no—
200C42—3562no—
201C23—894no—
202C23—1782no—
203C23—1782no—
204C23—1782no—
205C23—1782no—
206C23—1782no—
207C23—1782no—
208C23C23×D8911yescharacteristic
209D4—1788no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—892no—
223C2×C4—894no—
224C2×C4—892no—
225C2×C4—3568no—
226C2×C4—1781no—
227C2×C4—1781no—
228C2×C4—1782no—
229C2×C4—1782no—
230C2×C4—1782no—
231C2×C4—1782no—
232C2×C4—1781no—
233C2×C4—1781no—
234C2×C4—1781no—
235C2×C4—1781no—
236C2×C4D4×D8912yes—
237C22—3562no—
238C22—3562no—
239C22—3562no—
240C22—3562no—
241C22—1784no—
242C22—1784no—
243C22—1784no—
244C22C2×D4×D8911yescharacteristic
245C22#41×D8912yes—
246C22#41×D8912yes—
247C22#1566805811yescharacteristic
248C22#1566806011yescharacteristic
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—894no—
255C4—3561no—
256C4—3562no—
257C4—3561no—
258C4—1782no—
259C2—3564no—
260C2#1915210611yescharacteristic
261C2#124×D8911yescharacteristic
262C2#1915217811yescharacteristic
263C2#1915228012yes—
264C2#1915229912yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC22×D356C22
hypercenter#400D89
hypocenterC89#2562
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#15668002C2semidirect
3. #19151536C2semidirect
6. #19151490C2semidirect
7. #19151487C2semidirect
8. #19151457C2semidirect
9. #19151457C2semidirect
10. #19151449C2semidirect
11. #400×C89C2semidirect
133. C89#2562semidirect
137. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680022
C2×#156679742
#191515362
#191515162
#191515152
#191514902
#191514872
#191514572
#191514492
#400×C892
#256289