Finite Group Databasebeta

← #26031452

Subgroups — #26031452

Order 11392.

366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#19152155C211yesmaximal, characteristic, complemented
2#19152148C211yesmaximal, characteristic
3#19152007C212yesmaximal, complemented
4#19151963C212yesmaximal, complemented
5#19151923C214yesmaximal, complemented
6#19151889C212yesmaximal, complemented
7#19151879C212yesmaximal, complemented
8#432×C89C211yesmaximal, characteristic, complemented
9C2×#13083574—21no—
10#15668012C2211yescharacteristic
11#15668012C2211yescharacteristic
12#15668012C2211yescharacteristic
13#15668009C2211yescharacteristic
14#15668004C2212yes—
15#15668000—21no—
16#15667991—21no—
17#15667991—21no—
18#15667986—21no—
19#15667986C2212yes—
20C4×Dic178—21no—
21C4×Dic178—21no—
22C4×D356—21no—
23C4×D356C2212yes—
24#15667971C2212yes—
25#15667946C2214yes—
26#15667944C2214yes—
27#15667934C2214yes—
28#15667934C2214yes—
29C2×C42×C89C2211yescharacteristic
30C4⋊C8×C89C2212yes—
31C22⋊C8×C89C2212yes—
32#97×C89C2212yes—
33#13083574—44no—
34C2×Dic178—21no—
35C2×Dic178—21no—
36C2×Dic178—21no—
37C2×D356—21no—
38C2×D356—21no—
39C2×D356C2312yes—
40C2×C22⋊D89—22no—
41C2×C4×D89—22no—
42C4⋊Dic89—21no—
43C4⋊Dic89—21no—
44C4⋊Dic89—21no—
45C4⋊Dic89C2312yes—
46C4⋊Dic89C2312yes—
47C4⋊Dic89C2312yes—
48#13083553—22no—
49#13083553—22no—
50C22⋊Dic89—22no—
51#13083551—22no—
52#13083551—22no—
53C4×Dic89—22no—
54C22×C4×C89D411yescharacteristic
55C22×C4×C89D411yescharacteristic
56C22×C4×C89C2311yescharacteristic
57C2×C8×C89C2314yes—
58C42×C89D411yescharacteristic
59C42×C89D411yescharacteristic
60C42×C89C2311yescharacteristic
61C42×C89C2311yescharacteristic
62C23×C89C2×D411yescharacteristic
63C22×D89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—41no—
67C2×C4×C89C2×D411yescharacteristic
68C2×C4×C89C2×D411yescharacteristic
69C2×C4×C89C2×D411yescharacteristic
70C2×C4×C89C2×D411yescharacteristic
71C2×C4×C89C2×D411yescharacteristic
72C2×C4×C89C2411yescharacteristic
73C22⋊D89—44no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77D356—24no—
78D356—42no—
79D356—42no—
80C4×D89—44no—
81Dic178—42no—
82Dic178—42no—
83Dic178—42no—
84C8×C89—24no—
85C22×C89—21no—
86C22×C89—21no—
87C22×C89—21no—
88C22×C89C22×D411yescharacteristic
89C2×D89—42no—
90C2×D89—42no—
91C2×D89—42no—
92C4×C89—21no—
93C4×C89—21no—
94C4×C89—21no—
95C4×C89—21no—
96C4×C89AGL(1,ℤ/8)12yes—
97C4×C892−1+412yes—
98Dic89—42no—
99Dic89—42no—
100Dic89—42no—
101C2×C89—41no—
102C2×C89#53611yescharacteristic
103C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
104C2×C89#57511yescharacteristic
105D89—82no—
106#3235—891nomaximal, Sylow
107C89#323511yescharacteristic, complemented, Sylow
108#533—891no—
109#532—891no—
110#501—892no—
111#490—892no—
112#482—894no—
113#476—892no—
114#474—892no—
115#432D8911yescharacteristic, complemented
116C2×#41—1781no—
117C4⋊Q8—891no—
118C4⋊Q8—891no—
119C4⋊Q8—891no—
120#127—891no—
121#125—892no—
122#124—1781no—
123C22⋊Q8—1781no—
124C22⋊Q8—1781no—
125#121—892no—
126#121—1781no—
127C4×Q8—1781no—
128C4×Q8—1781no—
129C4×D4—892no—
130C4×D4—1781no—
131#117—892no—
132C2×C42C2×D8911yescharacteristic
133#107—894no—
134#106—894no—
135C4⋊C8C2×D8912yes—
136#102—894no—
137#102—894no—
138C22⋊C8C2×D8912yes—
139#97C2×D8912yes—
140#41—3564no—
141C2×Q8—1781no—
142C2×Q8—1781no—
143C2×Q8—1781no—
144C2×D4—892no—
145C2×D4—1782no—
146C2×D4—1781no—
147C2×D4—1781no—
148C22×C4—1782no—
149C22×C4D35611yescharacteristic
150C22×C4D35611yescharacteristic
151C22×C4C22×D8911yescharacteristic
152C2×C8C22×D8914yes—
153C4⋊C4—892no—
154C4⋊C4—892no—
155C4⋊C4—892no—
156C4⋊C4—1781no—
157C4⋊C4—1782no—
158C4⋊C4—1782no—
159C4⋊C4—1781no—
160C4⋊C4—1781no—
161C22⋊C4—1782no—
162C22⋊C4—1782no—
163C22⋊C4—1782no—
164C42—1782no—
165C42D35611yescharacteristic
166C42D35611yescharacteristic
167C42C22×D8911yescharacteristic
168C42C22×D8911yescharacteristic
169C23—1782no—
170C23C2×D35611yescharacteristic
171Q8—3562no—
172Q8—3562no—
173Q8—3562no—
174D4—3562no—
175D4—3562no—
176D4—3564no—
177D4—1784no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—3564no—
182C2×C4—1782no—
183C2×C4—1782no—
184C2×C4—1782no—
185C2×C4C2×D35611yescharacteristic
186C2×C4C2×D35611yescharacteristic
187C2×C4C2×D35611yescharacteristic
188C2×C4C2×D35611yescharacteristic
189C2×C4C2×D35611yescharacteristic
190C2×C4C23×D8911yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—3562no—
196C22—3562no—
197C22—3562no—
198C22C22×D35611yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—3562no—
204C4—3562no—
205C4—3562no—
206C4#1566804012yes—
207C4#1566805912yes—
208C2—41no—
209C2—7122no—
210C2#1915217411yescharacteristic
211C2C2×#1566804011yescharacteristic
212C2#1915239811yescharacteristic
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#432×C89C2
socleC22×C89C22×D4
prime radical#19152148C2
hypercenter#432D89
hypocenterC89#3235
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #19152155C2semidirect
3. #19152007C2semidirect
4. #19151963C2semidirect
5. #19151923C2semidirect
6. #19151889C2semidirect
7. #19151879C2semidirect
8. #432×C89C2semidirect
107. C89#3235semidirect
115. #432D89semidirect

Maximal subgroups

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

subgroupindex
#191521552
#191521482
#191520072
#191519632
#191519232
#191518892
#191518792
#432×C892
#323589