Finite Group Databasebeta

← #26024736

Subgroups — #26024736

Order 11392.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15667988C211yesmaximal, characteristic
2C2×C4⋊C4×D89C211yesmaximal, characteristic
3#19151539C214yesmaximal, complemented
4#19151505C211yesmaximal, characteristic, complemented
5#19151464C211yesmaximal, characteristic, complemented
6#19151463C211yesmaximal, characteristic, complemented
7#19151460C214yesmaximal
8C4×#13083551C211yesmaximal, characteristic
9#391×C89C211yesmaximal, characteristic, complemented
10C22×C4×D89C2212yes—
11C22×C4×D89C2211yescharacteristic
12#15667988—24no—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C4⋊C4×D89—24no—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×C4×Dic89C2211yescharacteristic
21#15667919C2212yes—
22#15667919C2214yes—
23#15667919C2214yes—
24#15667919C2214yes—
25C22×Q8×C89C2211yescharacteristic
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C42×C89C2211yescharacteristic
28#95×C89C2214yes—
29C23×D89C2311yescharacteristic
30C22×Dic89C2312yes—
31C22×Dic89C2312yes—
32C22×Dic89C2312yes—
33C22×Dic89C2311yescharacteristic
34C2×C4×D89—22no—
35C2×C4×D89—22no—
36C2×C4×D89—24no—
37C2×C4×D89—28no—
38C2×C4×D89D414yes—
39C4⋊Dic89—22no—
40C4⋊Dic89—22no—
41#13083553—24no—
42#13083553—24no—
43#13083551—24no—
44#13083551—24no—
45C4×Dic89—22no—
46C2×Q8×C89—22no—
47C2×Q8×C89—22no—
48C2×Q8×C89—22no—
49C22×C4×C89C2312yes—
50C22×C4×C89C2312yes—
51C22×C4×C89C2312yes—
52C22×C4×C89C2311yescharacteristic
53C4⋊C4×C89—22no—
54C42×C89—22no—
55C23×C89C2411yescharacteristic
56C22×D89—21no—
57C22×D89—21no—
58C22×D89—22no—
59C22×D89C2×D412yes—
60C22×D89#4114yes—
61Q8×C89—44no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—24no—
69C2×C4×C89—22no—
70C2×C4×C89C2×D412yes—
71C2×C4×C89#4112yes—
72C2×C4×C89#4112yes—
73C2×Dic89—21no—
74C2×Dic89—21no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—24no—
80C2×Dic89—24no—
81C2×Dic89—22no—
82C2×Dic89C2×D412yes—
83C4×D89—28no—
84C4×D89—48no—
85C22×C89C22×D411yescharacteristic
86C22×C89C2×#4111yescharacteristic
87C22×C89C2×#4111yescharacteristic
88C22×C89C2×#4112yes—
89C22×C892−1+412yes—
90C2×D89—22no—
91C2×D89—22no—
92C2×D89—24no—
93C2×D89—24no—
94C2×D89#12414yes—
95C4×C89—42no—
96C4×C89—42no—
97C4×C89—42no—
98C4×C89#12314yes—
99Dic89—22no—
100Dic89—42no—
101Dic89—42no—
102Dic89—42no—
103C2×C89C2×#12311yescharacteristic
104C2×C89C2×#12411yescharacteristic
105C2×C89#53611yescharacteristic
106C2×C89#55212yes—
107C2×C89#55212yes—
108D89—24no—
109#2503—891nomaximal, Sylow
110C89#250311yescharacteristic, complemented, Sylow
111C2×C22⋊Q8—891no—
112C22×C4⋊C4—891no—
113#400—894no—
114#391—891no—
115#391D8911yescharacteristic, complemented
116#382—891no—
117#382—891no—
118#381—894no—
119C4×C22⋊C4—891no—
120C22×Q8C2×D8911yescharacteristic
121C23×C4—891no—
122C23×C4—892no—
123C22⋊Q8—1784no—
124C2×C4⋊C4—891no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—891no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—1784no—
129C2×C4⋊C4C2×D8911yescharacteristic
130C2×C22⋊C4—892no—
131C2×C22⋊C4—892no—
132C2×C42—891no—
133C2×C42C2×D8911yescharacteristic
134#95—892no—
135#95—894no—
136#95—894no—
137#95—894no—
138#95C2×D8914yes—
139C24—891no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—891no—
144C22×C4—894no—
145C22×C4—892no—
146C22×C4—892no—
147C22×C4—892no—
148C22×C4—1784no—
149C22×C4—1788no—
150C22×C4—1782no—
151C22×C4—1782no—
152C22×C4C22×D8912yes—
153C22×C4C22×D8912yes—
154C22×C4C22×D8912yes—
155C22×C4C22×D8911yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—1784no—
158C4⋊C4—1784no—
159C4⋊C4—1782no—
160C4⋊C4—1782no—
161C22⋊C4—1784no—
162C22⋊C4—1784no—
163C42—22no—
164C42—1782no—
165C23—892no—
166C23—894no—
167C23—1781no—
168C23—1781no—
169C23—1782no—
170C23C23×D8911yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—892no—
181C2×C4—3568no—
182C2×C4—1782no—
183C2×C4—1782no—
184C2×C4—1782no—
185C2×C4—1784no—
186C2×C4—1782no—
187C2×C4—1784no—
188C2×C4—1782no—
189C2×C4—1781no—
190C2×C4—1781no—
191C2×C4—1788no—
192C2×C4D4×D8912yes—
193C2×C4#1308357312yes—
194C2×C4#1308357412yes—
195C22—894no—
196C22—1782no—
197C22—1784no—
198C22—1784no—
199C22—1782no—
200C22C2×D4×D8911yescharacteristic
201C22#41×D8912yes—
202C22C2×#1308357311yescharacteristic
203C22C2×#1308357411yescharacteristic
204C22#1566806012yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—3562no—
209C4—3562no—
210C4—3562no—
211C4—1782no—
212C4#1566799414yes—
213C2—1784no—
214C2C2×#1566799411yescharacteristic
215C2#124×D8911yescharacteristic
216C2#1915217311yescharacteristic
217C2#1915228212yes—
218C2#1915228912yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#391×C89C2
prime radicalC23×D89C23
hypercenter#391D89
hypocenterC89#2503
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #19151539C2semidirect
4. #19151505C2semidirect
5. #19151464C2semidirect
6. #19151463C2semidirect
9. #391×C89C2semidirect
110. C89#2503semidirect
115. #391D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679882
C2×C4⋊C4×D892
#191515392
#191515052
#191514642
#191514632
#191514602
C4×#130835512
#391×C892
#250389