Finite Group Databasebeta

← #26031391

Subgroups — #26031391

Order 11392.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#19152153C211yesmaximal, characteristic, complemented
2#19152149C211yesmaximal, characteristic
3#19151994C211yesmaximal, characteristic, complemented
4#19151946C211yesmaximal, characteristic, complemented
5#19151945C211yesmaximal, characteristic, complemented
6#19151925C214yesmaximal, complemented
7#19151901C214yesmaximal, complemented
8#19151649C211yesmaximal, characteristic, complemented
9#500×C89C211yesmaximal, characteristic, complemented
10C2×#13083575—21no—
11#15668012C2211yescharacteristic
12#15668009C2211yescharacteristic
13#15668003C2212yes—
14#15668001—21no—
15#15667992—21no—
16#15667988—21no—
17#15667987—21no—
18#15667987C2212yes—
19Q8×Dic89—21no—
20#15667977—21no—
21#15667974—21no—
22#15667974C2212yes—
23#15667970C2212yes—
24C42×D89C2211yescharacteristic
25#15667943C2214yes—
26#15667941C2212yes—
27#15667934C2214yes—
28#15667932C2214yes—
29#15667924C2212yes—
30C4×#10623494C2211yescharacteristic
31C4⋊Q8×C89C2211yescharacteristic
32C4⋊Q8×C89C2211yescharacteristic
33#107×C89C2214yes—
34C4×C8×C89C2211yescharacteristic
35#13083575—44no—
36C2×Dic178—21no—
37C2×D356—22no—
38C2×D356—21no—
39C2×D356—21no—
40C2×D356C2312yes—
41C2×C4×D89—22no—
42C2×C4×D89D411yescharacteristic
43C2×C4×D89D411yescharacteristic
44C2×C4×D89C2311yescharacteristic
45C2×#10623494C2312yes—
46C4⋊Dic89—21no—
47C4⋊Dic89—22no—
48C4⋊Dic89C2312yes—
49#13083553—22no—
50#13083551—22no—
51#13083551—22no—
52#13083551—22no—
53C4×Dic89—22no—
54C4×Dic89D411yescharacteristic
55C4×Dic89D411yescharacteristic
56C4×Dic89C2311yescharacteristic
57C2×Q8×C89—21no—
58C2×Q8×C89—21no—
59C2×C8×C89C2312yes—
60C4⋊C4×C89—21no—
61C4⋊C4×C89—21no—
62C4⋊C4×C89C2312yes—
63C4⋊C4×C89C2312yes—
64C42×C89C2311yescharacteristic
65C22×D89—22no—
66C22×D89C2×D411yescharacteristic
67Q8×C89—42no—
68Q8×C89—42no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89C2×D411yescharacteristic
72C2×C4×C89C2×D411yescharacteristic
73C2×C4×C89C2411yescharacteristic
74C2×Dic89—22no—
75C2×Dic89C2×D411yescharacteristic
76C2×Dic89C2×D411yescharacteristic
77C2×Dic89C2×D411yescharacteristic
78D356—24no—
79D356—44no—
80D356—42no—
81D356—42no—
82C4×D89—22no—
83C4×D89—22no—
84C4×D89—22no—
85C4×D89—44no—
86Dic178—42no—
87C8×C89—22no—
88#10623494—22no—
89C22×C89C22×D411yescharacteristic
90C2×D89—21no—
91C2×D89—21no—
92C2×D89—21no—
93C2×D89—42no—
94C2×D89—42no—
95C2×D89—42no—
96C4×C89—42no—
97C4×C89—42no—
98C4×C89#13512yes—
99C4×C89AGL(1,ℤ/8)12yes—
100C4×C892−1+412yes—
101Dic89—21no—
102Dic89—21no—
103Dic89—21no—
104Dic89—42no—
105C2×C89#53611yescharacteristic
106C2×C89C2×#13511yescharacteristic
107C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
108D89—41no—
109D89—82no—
110#3228—891nomaximal, Sylow
111C89#322811yescharacteristic, complemented, Sylow
112#533—891no—
113#532—891no—
114#500D8911yescharacteristic, complemented
115#498—891no—
116#486—891no—
117#486—891no—
118#482—894no—
119#478—894no—
120#431—891no—
121C2×#41—1781no—
122C4⋊Q8—891no—
123C4⋊Q8C2×D8911yescharacteristic
124C4⋊Q8C2×D8911yescharacteristic
125#127—891no—
126#125—892no—
127#124—1781no—
128C22⋊Q8—1781no—
129C22⋊Q8—1781no—
130#121—892no—
131#121—1781no—
132C4×Q8—1781no—
133C4×Q8—1781no—
134C4×D4—892no—
135C4×D4—1781no—
136#117—892no—
137C2×C42—891no—
138#107C2×D8914yes—
139#106—894no—
140C4⋊C8—892no—
141#102—894no—
142#102—894no—
143C22⋊C8—892no—
144C4×C8—891no—
145C4×C8C2×D8911yescharacteristic
146#41—3564no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—1781no—
150C2×D4—892no—
151C2×D4—1782no—
152C2×D4—1781no—
153C2×D4—1781no—
154C22×C4—891no—
155C22×C4—891no—
156C22×C4—891no—
157C22×C4—1782no—
158C2×C8—892no—
159C2×C8C22×D8912yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—892no—
163C4⋊C4—1782no—
164C4⋊C4—1782no—
165C4⋊C4—1781no—
166C4⋊C4C22×D8912yes—
167C4⋊C4C22×D8912yes—
168C22⋊C4—1782no—
169C22⋊C4—1782no—
170C22⋊C4—1782no—
171C42—891no—
172C42—891no—
173C42—891no—
174C42—1782no—
175C42C22×D8911yescharacteristic
176C23—891no—
177C23—1782no—
178Q8—42no—
179Q8—42no—
180Q8—3562no—
181D4—3564no—
182D4—3562no—
183D4—3562no—
184D4—1784no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—891no—
188C2×C4—891no—
189C2×C4—891no—
190C2×C4—3564no—
191C2×C4—1782no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4D4×D8911yescharacteristic
196C2×C4D4×D8911yescharacteristic
197C2×C4C23×D8911yescharacteristic
198C8—22no—
199C8—1782no—
200C22—3562no—
201C22—3562no—
202C22—3562no—
203C22—1781no—
204C22—1781no—
205C22—1781no—
206C22C2×D4×D8911yescharacteristic
207C4—42no—
208C4—42no—
209C4—3562no—
210C4—1781no—
211C4—1781no—
212C4—1781no—
213C4#1566803512yes—
214C4#1566803612yes—
215C4#1566806012yes—
216C2—3561no—
217C2—7122no—
218C2#1915217311yescharacteristic
219C2C2×#1566803511yescharacteristic
220C2C2×#1566803611yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#500×C89C2
socleC22×C89C22×D4
prime radical#19152149C2
hypercenter#500D89
hypocenterC89#3228
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #19152153C2semidirect
3. #19151994C2semidirect
4. #19151946C2semidirect
5. #19151945C2semidirect
6. #19151925C2semidirect
7. #19151901C2semidirect
8. #19151649C2semidirect
9. #500×C89C2semidirect
111. C89#3228semidirect
114. #500D89semidirect

Maximal subgroups

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

subgroupindex
#191521532
#191521492
#191519942
#191519462
#191519452
#191519252
#191519012
#191516492
#500×C892
#322889