Finite Group Databasebeta

← #26023542

Subgroups — #26023542

Order 11392.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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
2C2×#15667977C211yesmaximal, characteristic
3#19151531C212yesmaximal
4#19151530C211yesmaximal, characteristic
5#19151528C211yesmaximal, characteristic
6#19151519C212yesmaximal
7#19151517C211yesmaximal, characteristic
8C4⋊C4×Dic89C212yesmaximal
9#19151449C212yesmaximal
10#19151443C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic
12C22×Dic178C2211yescharacteristic
13Q8×Dic89—24no—
14#15667977—24no—
15C2×C4⋊Dic89C2212yes—
16C2×C4⋊Dic89C2212yes—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×C4×Dic89C2211yescharacteristic
23C2×C4×Dic89C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25C2×C4×Dic89C2211yescharacteristic
26C2×C4×Dic89C2212yes—
27#15667919C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C22×Q8×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2212yes—
34C2×C4⋊C4×C89C2211yescharacteristic
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C2×Dic178—22no—
38C2×Dic178—22no—
39C2×Dic178—22no—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2312yes—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C4⋊Dic89—22no—
47C4⋊Dic89—24no—
48C4⋊Dic89—24no—
49#13083553—22no—
50#13083553—24no—
51#13083553—24no—
52#13083553—22no—
53C4×Dic89—22no—
54C4×Dic89—22no—
55C4×Dic89—24no—
56C4×Dic89D414yes—
57C4×Dic89Q818yescomplemented
58C2×Q8×C89—22no—
59C2×Q8×C89—24no—
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2312yes—
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2312yes—
65C4⋊C4×C89—22no—
66C4⋊C4×C89—24no—
67C23×C89C2411yescharacteristic
68Q8×C89—28no—
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×C89C2×D412yes—
79C2×C4×C89C2×Q814yes—
80C2×C4×C89#4114yes—
81C2×C4×C89#4112yes—
82C2×Dic89—21no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—21no—
86C2×Dic89—21no—
87C2×Dic89—21no—
88C2×Dic89—21no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89C2×D412yes—
94C2×Dic89C2×D412yes—
95C2×Dic89C2×Q814yes—
96C2×Dic89C2×Q814yes—
97C2×Dic89#4112yes—
98Dic178—28no—
99C22×C89C22×D411yescharacteristic
100C22×C89C22×Q812yes—
101C22×C89C2×#4111yescharacteristic
102C22×C89C2×#4112yes—
103C22×C89C2×#4111yescharacteristic
104C4×C89—22no—
105C4×C89—22no—
106C4×C89—24no—
107C4×C89—24no—
108C4×C89—41no—
109Dic89—22no—
110Dic89—22no—
111Dic89—24no—
112Dic89—41no—
113Dic89—42no—
114Dic89C4⋊Q814yes—
115C2×C89#52511yescharacteristic
116C2×C89#52511yescharacteristic
117C2×C89C2×C4⋊Q811yescharacteristic
118C2×C89#53312yes—
119C2×C89#53312yes—
120#2399—891nomaximal, Sylow
121C89#239911yescharacteristic, complemented, Sylow
122C2×C4×Q8—891no—
123C2×C4×Q8—891no—
124#398—891no—
125#398—892no—
126#398—891no—
127#395—891no—
128#395—892no—
129#395D8911yescharacteristic
130C4×C4⋊C4—892no—
131C4×C4⋊C4—892no—
132#376—891no—
133C22×Q8—891no—
134C22×Q8C2×D8911yescharacteristic
135C4×Q8—1784no—
136C4×Q8—1784no—
137C2×C4⋊C4—891no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—891no—
140C2×C4⋊C4—891no—
141C2×C4⋊C4—892no—
142C2×C4⋊C4—892no—
143C2×C4⋊C4—892no—
144C2×C4⋊C4C2×D8911yescharacteristic
145C2×C4⋊C4C2×D8912yes—
146C2×C42—891no—
147C2×C42—892no—
148C2×C42—891no—
149C2×C42—892no—
150C2×C42—891no—
151#95—891no—
152#95—892no—
153#95—892no—
154#95—892no—
155#95—892no—
156#95C2×D8911yescharacteristic
157#95C2×D8912yes—
158C2×Q8—22no—
159C2×Q8—24no—
160C2×Q8—1782no—
161C2×Q8—1782no—
162C2×Q8—1782no—
163C22×C4—891no—
164C22×C4—892no—
165C22×C4—891no—
166C22×C4—891no—
167C22×C4—892no—
168C22×C4—891no—
169C22×C4C22×D8911yescharacteristic
170C22×C4C22×D8911yescharacteristic
171C22×C4C22×D8912yes—
172C22×C4C22×D8912yes—
173C22×C4C22×D8911yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—1782no—
177C4⋊C4—1784no—
178C4⋊C4—1784no—
179C4⋊C4—1782no—
180C4⋊C4—1782no—
181C4⋊C4—1784no—
182C4⋊C4—1784no—
183C42—894no—
184C42—898no—
185C42—1782no—
186C42—1784no—
187C42—1782no—
188C23C23×D8911yescharacteristic
189Q8—28no—
190Q8—1788no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—892no—
201C2×C4—894no—
202C2×C4—892no—
203C2×C4—894no—
204C2×C4—892no—
205C2×C4—1781no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4—1781no—
211C2×C4—1781no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1781no—
215C2×C4—1781no—
216C2×C4D4×D8912yes—
217C2×C4Q8×D8914yes—
218C2×C4#1308357314yes—
219C2×C4#1308357512yes—
220C22C2×D4×D8911yescharacteristic
221C22C2×Q8×D8912yes—
222C22#41×D8911yescharacteristic
223C22C2×#1308357312yes—
224C22C2×#1308357511yescharacteristic
225C4—24no—
226C4—22no—
227C4—24no—
228C4—22no—
229C4—41no—
230C4—894no—
231C4—3561no—
232C4—3562no—
233C4—1784no—
234C4—1782no—
235C4—1782no—
236C2#1915210411yescharacteristic
237C2#1915211111yescharacteristic
238C2C4⋊Q8×D8911yescharacteristic
239C2#1915215012yes—
240C2#1915215312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#395×C89C2
hypercenter#395D89
hypocenterC89#2399
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
57. C4×Dic89Q8semidirect
121. C89#2399semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic892
C2×#156679772
#191515312
#191515302
#191515282
#191515192
#191515172
C4⋊C4×Dic892
#191514492
#191514432
#395×C892
#239989