Finite Group Databasebeta

← #26023523

Subgroups — #26023523

Order 11392.

528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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×Q8×Dic89C211yesmaximal, characteristic, complemented
2C2×#15667970C211yesmaximal, characteristic
3#19151537C211yesmaximal, characteristic, complemented
4#19151535C211yesmaximal, characteristic
5#19151530C212yesmaximal, complemented
6#19151520C212yesmaximal
7#19151509C211yesmaximal, characteristic
8C4⋊C4×Dic89C212yesmaximal, complemented
9#19151449C211yesmaximal, characteristic, complemented
10#19151445C212yesmaximal
11#395×C89C211yesmaximal, characteristic, complemented
12C22×C4×D89C2211yescharacteristic
13Q8×Dic89—24no—
14#15667970—24no—
15C2×C4⋊Dic89C2212yes—
16C2×C4⋊Dic89C2212yes—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2211yescharacteristic
23C2×#13083551C2211yescharacteristic
24C2×C4×Dic89C2212yes—
25C2×C4×Dic89C2212yes—
26C2×C4×Dic89C2211yescharacteristic
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C22×Q8×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2212yes—
34C2×C4⋊C4×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2211yescharacteristic
37C23×D89C2311yescharacteristic
38C22×Dic89C2312yes—
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C2×C4×D89—22no—
44C2×C4×D89—22no—
45C2×C4×D89Q814yescomplemented
46C4⋊Dic89—22no—
47C4⋊Dic89—24no—
48C4⋊Dic89—22no—
49C4⋊Dic89—24no—
50#13083553—24no—
51#13083551—22no—
52#13083551—24no—
53#13083551—24no—
54#13083551—22no—
55C4×Dic89—22no—
56C4×Dic89—24no—
57C4×Dic89—24no—
58C4×Dic89D414yes—
59C2×Q8×C89—22no—
60C2×Q8×C89—24no—
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2312yes—
65C22×C4×C89C2312yes—
66C4⋊C4×C89—22no—
67C4⋊C4×C89—24no—
68C23×C89C2411yescharacteristic
69C22×D89—21no—
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—21no—
73C22×D89C2×Q812yes—
74Q8×C89—28no—
75C2×C4×C89—21no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—21no—
82C2×C4×C89—21no—
83C2×C4×C89—22no—
84C2×C4×C89C2×D412yes—
85C2×C4×C89C2×Q812yes—
86C2×C4×C89#4114yes—
87C2×C4×C89#4114yes—
88C2×Dic89—22no—
89C2×Dic89—21no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89C2×D412yes—
98C2×Dic89C2×D412yes—
99C2×Dic89C2×Q812yes—
100C2×Dic89#4112yes—
101C4×D89—28no—
102C22×C89C22×D411yescharacteristic
103C22×C89C22×Q811yescharacteristic
104C22×C89C2×#4111yescharacteristic
105C22×C89C2×#4112yes—
106C22×C89C2×#4112yes—
107C2×D89—22no—
108C2×D89—24no—
109C2×D89—41no—
110C2×D89—42no—
111C2×D89—41no—
112C4×C89—22no—
113C4×C89—22no—
114C4×C89—24no—
115C4×C89—24no—
116C4×C89—41no—
117Dic89—22no—
118Dic89—42no—
119Dic89—41no—
120Dic89—42no—
121Dic89C22⋊Q814yes—
122C2×C89C2×C22⋊Q811yescharacteristic
123C2×C89#52511yescharacteristic
124C2×C89#52912yes—
125C2×C89#53211yescharacteristic
126C2×C89#53312yes—
127D89—42no—
128#2396—891nomaximal, Sylow
129C89#239611yescharacteristic, complemented, Sylow
130C2×C4×Q8—891no—
131C2×#117—891no—
132#400—891no—
133#399—891no—
134#398—892no—
135#396—892no—
136#395D8911yescharacteristic, complemented
137#393—891no—
138C4×C4⋊C4—892no—
139C4×C4⋊C4—891no—
140C4×C22⋊C4—892no—
141C22×Q8C2×D8911yescharacteristic
142C23×C4—891no—
143C4×Q8—1784no—
144#117—1784no—
145C2×C4⋊C4—891no—
146C2×C4⋊C4—892no—
147C2×C4⋊C4—891no—
148C2×C4⋊C4—892no—
149C2×C4⋊C4—892no—
150C2×C4⋊C4C2×D8911yescharacteristic
151C2×C4⋊C4C2×D8912yes—
152C2×C22⋊C4—891no—
153C2×C22⋊C4—891no—
154C2×C22⋊C4—892no—
155C2×C22⋊C4—892no—
156C2×C42—891no—
157C2×C42—891no—
158C2×C42—892no—
159C2×C42—892no—
160#95—892no—
161#95—892no—
162#95—891no—
163#95—892no—
164#95C2×D8912yes—
165#95C2×D8911yescharacteristic
166C24—891no—
167C2×Q8—22no—
168C2×Q8—24no—
169C22×C4—891no—
170C22×C4—891no—
171C22×C4—894no—
172C22×C4—892no—
173C22×C4—891no—
174C22×C4—892no—
175C22×C4—1782no—
176C22×C4—1782no—
177C22×C4C22×D8911yescharacteristic
178C22×C4C22×D8911yescharacteristic
179C22×C4C22×D8911yescharacteristic
180C22×C4C22×D8912yes—
181C22×C4C22×D8912yes—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—1782no—
185C4⋊C4—1784no—
186C4⋊C4—1782no—
187C4⋊C4—1784no—
188C4⋊C4—1784no—
189C22⋊C4—1782no—
190C22⋊C4—1782no—
191C22⋊C4—1784no—
192C22⋊C4—1784no—
193C42—894no—
194C42—1782no—
195C42—1784no—
196C42—1784no—
197C23—892no—
198C23—1781no—
199C23—1781no—
200C23—1782no—
201C23—1782no—
202C23C23×D8911yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—892no—
214C2×C4—892no—
215C2×C4—892no—
216C2×C4—892no—
217C2×C4—1788no—
218C2×C4—1781no—
219C2×C4—1782no—
220C2×C4—1782no—
221C2×C4—1782no—
222C2×C4—1782no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4D4×D8912yes—
228C2×C4Q8×D8912yes—
229C2×C4#1308357314yes—
230C2×C4#1308357514yes—
231C22—3562no—
232C22—3561no—
233C22—3561no—
234C22—1784no—
235C22—1782no—
236C22C2×D4×D8911yescharacteristic
237C22C2×Q8×D8911yescharacteristic
238C22#41×D8911yescharacteristic
239C22C2×#1308357312yes—
240C22C2×#1308357512yes—
241C4—24no—
242C4—22no—
243C4—22no—
244C4—24no—
245C4—41no—
246C4—894no—
247C4—3562no—
248C4—3561no—
249C4—3562no—
250C4—1782no—
251C2—3562no—
252C2C22⋊Q8×D8911yescharacteristic
253C2#1915210411yescharacteristic
254C2#1915213412yes—
255C2#1915214911yescharacteristic
256C2#1915215312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#395×C89C2
prime radicalC23×D89C23
hypercenter#395D89
hypocenterC89#2396
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic89C2semidirect
3. #19151537C2semidirect
5. #19151530C2semidirect
8. C4⋊C4×Dic89C2semidirect
9. #19151449C2semidirect
11. #395×C89C2semidirect
45. C2×C4×D89Q8semidirect
129. C89#2396semidirect
136. #395D89semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic892
C2×#156679702
#191515372
#191515352
#191515302
#191515202
#191515092
C4⋊C4×Dic892
#191514492
#191514452
#395×C892
#239689