Finite Group Databasebeta

← #26025884

Subgroups — #26025884

Order 11392.

470 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15668006C211yesmaximal, characteristic
2#19151536C211yesmaximal, characteristic, complemented
3#19151533C211yesmaximal, characteristic
4#19151517C211yesmaximal, characteristic, complemented
5#19151509C211yesmaximal, characteristic
6#19151493C212yesmaximal, complemented
7#19151489C212yesmaximal
8#19151488C212yesmaximal
9#19151482C212yesmaximal, complemented
10#19151444C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C89C211yesmaximal, characteristic, complemented
12#15668006—24no—
13C2×#13083553C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2211yescharacteristic
17C2×#13083553C2211yescharacteristic
18C2×#13083551C2211yescharacteristic
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2211yescharacteristic
22C2×#13083551C2211yescharacteristic
23C2×C4×Dic89C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2211yescharacteristic
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31C22×Q8×C89C2211yescharacteristic
32C4×Q8×C89—24no—
33C2×C4⋊C4×C89C2212yes—
34C2×C4⋊C4×C89C2211yescharacteristic
35C2×C42×C89C2212yes—
36C2×C42×C89C2211yescharacteristic
37C23×D89C2311yescharacteristic
38C22×Dic89C2312yes—
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2312yes—
43#13083553—22no—
44#13083553—22no—
45#13083553—22no—
46#13083553—24no—
47#13083553—24no—
48#13083551—22no—
49#13083551—22no—
50#13083551—22no—
51#13083551—24no—
52#13083551—24no—
53C4×Dic89—24no—
54C2×Q8×C89—22no—
55C2×Q8×C89—24no—
56C22×C4×C89C2312yes—
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2312yes—
61C4⋊C4×C89—24no—
62C4⋊C4×C89—22no—
63C42×C89—24no—
64C42×C89D414yes—
65C23×C89C2411yescharacteristic
66C22×D89—21no—
67C22×D89—22no—
68C22×D89—22no—
69C22×D89—21no—
70C22×D89—21no—
71Q8×C89—28no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—21no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89C2×D412yes—
82C2×C4×C89C2×D412yes—
83C2×C4×C89C2×D412yes—
84C2×C4×C89#4114yes—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—21no—
88C2×Dic89—21no—
89C2×Dic89—21no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—21no—
95C2×Dic89—21no—
96C2×Dic89—22no—
97C2×Dic89#4114yes—
98C22×C89C22×D411yescharacteristic
99C22×C89C2×#4112yes—
100C22×C89C2×#4112yes—
101C22×C892−1+411yescharacteristic
102C22×C892−1+411yescharacteristic
103C2×D89—41no—
104C2×D89—41no—
105C2×D89—41no—
106C2×D89—42no—
107C2×D89—42no—
108C4×C89—22no—
109C4×C89—24no—
110C4×C89—22no—
111C4×C89—22no—
112C4×C89—42no—
113Dic89—24no—
114Dic89—41no—
115Dic89—41no—
116Dic89—41no—
117Dic89—42no—
118C2×C89#52511yescharacteristic
119C2×C89#53211yescharacteristic
120C2×C89#53611yescharacteristic
121C2×C89#55212yes—
122C2×C89#55612yes—
123D89—81no—
124#2604—891nomaximal, Sylow
125C89#260411yescharacteristic, complemented, Sylow
126C2×#126—891no—
127C2×C4×Q8D8911yescharacteristic, complemented
128#400—891no—
129#399—891no—
130#395—891no—
131#393—891no—
132#389—892no—
133#388—892no—
134#388—892no—
135#387—892no—
136#376—891no—
137C22×Q8C2×D8911yescharacteristic
138#126—1784no—
139C4×Q8—24no—
140C2×C4⋊C4—891no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—891no—
143C2×C4⋊C4—892no—
144C2×C4⋊C4—892no—
145C2×C4⋊C4C2×D8912yes—
146C2×C4⋊C4C2×D8911yescharacteristic
147C2×C22⋊C4—891no—
148C2×C22⋊C4—891no—
149C2×C22⋊C4—891no—
150C2×C22⋊C4—892no—
151C2×C22⋊C4—892no—
152C2×C42—892no—
153C2×C42C2×D8912yes—
154C2×C42C2×D8911yescharacteristic
155#95—892no—
156#95—891no—
157#95—891no—
158#95—892no—
159#95—892no—
160#95—892no—
161#95—892no—
162C24—891no—
163C2×Q8—22no—
164C2×Q8—24no—
165C22×C4—892no—
166C22×C4—892no—
167C22×C4—891no—
168C22×C4—891no—
169C22×C4—891no—
170C22×C4C22×D8912yes—
171C22×C4C22×D8911yescharacteristic
172C22×C4C22×D8911yescharacteristic
173C22×C4C22×D8911yescharacteristic
174C22×C4C22×D8912yes—
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—1784no—
178C4⋊C4—1782no—
179C4⋊C4—1782no—
180C4⋊C4—1782no—
181C4⋊C4—1784no—
182C22⋊C4—1784no—
183C22⋊C4—1782no—
184C22⋊C4—1782no—
185C22⋊C4—1782no—
186C22⋊C4—1784no—
187C42—24no—
188C42—1784no—
189C42C22⋊D8914yes—
190C23—1781no—
191C23—1782no—
192C23—1782no—
193C23—1781no—
194C23—1781no—
195C23C23×D8911yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—894no—
207C2×C4—1781no—
208C2×C4—1781no—
209C2×C4—1781no—
210C2×C4—1782no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1781no—
215C2×C4—1781no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1782no—
219C2×C4C2×C22⋊D8912yes—
220C2×C4C2×C22⋊D8912yes—
221C2×C4C2×C22⋊D8912yes—
222C2×C4#1308357414yes—
223C22—3561no—
224C22—3561no—
225C22—3562no—
226C22—3562no—
227C22—3561no—
228C22C22×C22⋊D8911yescharacteristic
229C22#41×D8912yes—
230C22C2×#1308357412yes—
231C22#1566806011yescharacteristic
232C22#1566806011yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—24no—
237C4—42no—
238C4—3561no—
239C4—3561no—
240C4—3562no—
241C4—3561no—
242C4—1784no—
243C2—7121no—
244C2#1915210911yescharacteristic
245C2#1915214411yescharacteristic
246C2#1915217211yescharacteristic
247C2#1915228912yes—
248C2#1915232012yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
FittingC2×C4×Q8×C89C2
prime radicalC23×D89C23
hypercenterC2×C4×Q8D89
hypocenterC89#2604
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #19151536C2semidirect
4. #19151517C2semidirect
6. #19151493C2semidirect
9. #19151482C2semidirect
10. #19151444C2semidirect
11. C2×C4×Q8×C89C2semidirect
125. C89#2604semidirect
127. C2×C4×Q8D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680062
#191515362
#191515332
#191515172
#191515092
#191514932
#191514892
#191514882
#191514822
#191514442
C2×C4×Q8×C892
#260489