Finite Group Databasebeta

← #26028283

Subgroups — #26028283

Order 11392.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15667990C211yesmaximal, characteristic, complemented
2C2×#15667983C211yesmaximal, characteristic
3#19151534C212yesmaximal, complemented
4#19151530C211yesmaximal, characteristic, complemented
5#19151528C211yesmaximal, characteristic, complemented
6#19151514C212yesmaximal, complemented
7#19151513C212yesmaximal, complemented
8#19151512C211yesmaximal, characteristic, complemented
9#19151510C212yesmaximal, complemented
10#19151460C211yesmaximal, characteristic, complemented
11#394×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×C22⋊D89C2212yes—
14C22×C4×D89C2211yescharacteristic
15#15667990—24no—
16#15667983—24no—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2212yes—
22C2×C22⋊Dic89C2212yes—
23C2×C22⋊Dic89C2212yes—
24C2×C22⋊Dic89C2212yes—
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2212yes—
28#15667919C2212yes—
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C22×D4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2212yes—
35C2×C22⋊C4×C89C2212yes—
36#95×C89C2211yescharacteristic
37C23×D89C2311yescharacteristic
38C2×Dic178—22no—
39C2×Dic178—42no—
40C2×C22⋊D89—24no—
41C2×C22⋊D89—42no—
42C2×C22⋊D89—42no—
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2312yes—
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48C2×C4×D89—42no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51C4⋊Dic89—42no—
52#13083553—22no—
53#13083553—22no—
54#13083553—42no—
55C22⋊Dic89—24no—
56C22⋊Dic89—42no—
57C22⋊Dic89—42no—
58#13083551—22no—
59#13083551—22no—
60#13083551—42no—
61C24×C89C2312yes—
62C2×D4×C89—22no—
63C2×D4×C89—42no—
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2312yes—
66C22×C4×C89C2311yescharacteristic
67C22×C4×C89C2311yescharacteristic
68C4⋊C4×C89—22no—
69C22⋊C4×C89—42no—
70C22⋊C4×C89—42no—
71C23×C89—22no—
72C23×C89—22no—
73C23×C89—22no—
74C23×C89—22no—
75C23×C89—22no—
76C23×C89—22no—
77C23×C89—22no—
78C23×C89C2411yescharacteristic
79C22×D89—22no—
80C22×D89—21no—
81C22×D89—21no—
82C22×D89—22no—
83C22×D89C2×D412yes—
84D4×C89—44no—
85C2×C4×C89—22no—
86C2×C4×C89—21no—
87C2×C4×C89—21no—
88C2×C4×C89—21no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89—21no—
93C2×C4×C89—22no—
94C2×C4×C89C2×D412yes—
95C22⋊D89—48no—
96C2×Dic89—22no—
97C2×Dic89—21no—
98C2×Dic89—21no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—21no—
102C2×Dic89—22no—
103C2×Dic89—22no—
104C2×Dic89—22no—
105C2×Dic89—21no—
106C2×Dic89—22no—
107C2×Dic89—22no—
108C2×Dic89C2×D412yes—
109C4×D89—44no—
110Dic178—44no—
111C22×C89—42no—
112C22×C89—42no—
113C22×C89—42no—
114C22×C89—42no—
115C22×C89—42no—
116C22×C89—42no—
117C22×C89—42no—
118C22×C89C22×D411yescharacteristic
119C22×C89H(5,𝔽2)12yes—
120C22×C89H(5,𝔽2)11yescharacteristic
121C22×C89H(5,𝔽2)11yescharacteristic
122C22×C892−1+412yes—
123C2×D89—22no—
124C2×D89—22no—
125C2×D89—22no—
126C2×D89—42no—
127C2×D89—42no—
128C4×C89—22no—
129C4×C89—41no—
130C4×C89—41no—
131C4×C89—42no—
132Dic89—22no—
133Dic89—41no—
134Dic89—41no—
135Dic89—42no—
136Dic89—42no—
137C2×C89—82no—
138C2×C89#53411yescharacteristic
139C2×C89#53511yescharacteristic
140C2×C89#53611yescharacteristic
141C2×C89#56212yes—
142C2×C89#56212yes—
143D89—42no—
144#2816—891nomaximal, Sylow
145C89#281611yescharacteristic, complemented, Sylow
146C2×C22⋊Q8—891no—
147C2×#121—891no—
148#399—892no—
149#398—891no—
150#398—891no—
151#394—891no—
152#394—892no—
153#394—892no—
154#394D8911yescharacteristic, complemented
155#393—892no—
156#381—891no—
157C22×Q8—891no—
158C22×D4—892no—
159C22×D4C2×D8911yescharacteristic
160C23×C4—891no—
161C22⋊Q8—1784no—
162#121—1784no—
163C2×C4⋊C4—892no—
164C2×C4⋊C4—892no—
165C2×C4⋊C4—891no—
166C2×C4⋊C4—891no—
167C2×C4⋊C4—891no—
168C2×C4⋊C4C2×D8911yescharacteristic
169C2×C22⋊C4—892no—
170C2×C22⋊C4—892no—
171C2×C22⋊C4—892no—
172C2×C22⋊C4—892no—
173C2×C22⋊C4—891no—
174C2×C22⋊C4—891no—
175C2×C22⋊C4C2×D8912yes—
176C2×C22⋊C4C2×D8912yes—
177#95—892no—
178#95—891no—
179#95—892no—
180#95—892no—
181#95C2×D8911yescharacteristic
182C24—891no—
183C24C22×D8912yes—
184C2×Q8—3562no—
185C2×Q8—1782no—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—3562no—
189C2×D4—3562no—
190C2×D4—1784no—
191C22×C4—891no—
192C22×C4—894no—
193C22×C4—892no—
194C22×C4—891no—
195C22×C4—892no—
196C22×C4—891no—
197C22×C4—3562no—
198C22×C4C22×D8912yes—
199C22×C4C22×D8911yescharacteristic
200C22×C4C22×D8911yescharacteristic
201C22×C4C22×D8911yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—3562no—
204C4⋊C4—3562no—
205C4⋊C4—1782no—
206C4⋊C4—1782no—
207C4⋊C4—1782no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—3562no—
211C22⋊C4—3562no—
212C22⋊C4—3562no—
213C22⋊C4—1782no—
214C22⋊C4—1782no—
215C22⋊C4—1784no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—892no—
224C23—1782no—
225C23—1781no—
226C23—1781no—
227C23—1782no—
228C23C23×D8911yescharacteristic
229Q8—3564no—
230D4—44no—
231D4—3568no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—892no—
242C2×C4—3564no—
243C2×C4—1781no—
244C2×C4—1782no—
245C2×C4—1781no—
246C2×C4—1782no—
247C2×C4—1782no—
248C2×C4—1781no—
249C2×C4—1782no—
250C2×C4—1781no—
251C2×C4—1782no—
252C2×C4—1782no—
253C2×C4—1782no—
254C2×C4—1782no—
255C2×C4D4×D8912yes—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—3562no—
264C22—3562no—
265C22—1782no—
266C22—1782no—
267C22—1782no—
268C22C2×D4×D8911yescharacteristic
269C22#1566805712yes—
270C22#1566805711yescharacteristic
271C22#1566805811yescharacteristic
272C22#1566805912yes—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—42no—
277C4—3561no—
278C4—3562no—
279C4—3561no—
280C4—3562no—
281C4—1782no—
282C2—82no—
283C2—3562no—
284C2#1915215811yescharacteristic
285C2#1915216411yescharacteristic
286C2#1915216811yescharacteristic
287C2#1915234312yes—
288C2#1915234512yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#394×C89C2
prime radicalC2×#15667983C2
hypercenter#394D89
hypocenterC89#2816
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#15667990C2semidirect
3. #19151534C2semidirect
4. #19151530C2semidirect
5. #19151528C2semidirect
6. #19151514C2semidirect
7. #19151513C2semidirect
8. #19151512C2semidirect
9. #19151510C2semidirect
10. #19151460C2semidirect
11. #394×C89C2semidirect
145. C89#2816semidirect
154. #394D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679902
C2×#156679832
#191515342
#191515302
#191515282
#191515142
#191515132
#191515122
#191515102
#191514602
#394×C892
#281689