Finite Group Databasebeta

← #26031381

Subgroups — #26031381

Order 11392.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#19152149C211yesmaximal, characteristic
2C4⋊Q8×D89C211yesmaximal, characteristic, complemented
3#19151994C211yesmaximal, characteristic, complemented
4#19151946C211yesmaximal, characteristic, complemented
5#19151945C211yesmaximal, characteristic, complemented
6#19151918C214yesmaximal, complemented
7#19151887C214yesmaximal, complemented
8#19151649C211yesmaximal, characteristic, complemented
9#498×C89C211yesmaximal, characteristic, complemented
10C2×#13083575—21no—
11C2×Q8×D89—21no—
12#15668012C2211yescharacteristic
13#15668011—21no—
14#15668011C2212yes—
15#15668010—21no—
16#15668009C2211yescharacteristic
17#15668001—21no—
18#15667987—21no—
19#15667987C2212yes—
20#15667974—21no—
21#15667974C2212yes—
22C4⋊C4×D89—21no—
23C4⋊C4×D89C2212yes—
24C42×D89C2211yescharacteristic
25#15667943C2214yes—
26#15667941C2212yes—
27#15667934C2214yes—
28#15667932C2214yes—
29#15667924C2212yes—
30C4×#10623494C2211yescharacteristic
31C4⋊Q8×C89C2211yescharacteristic
32C4⋊Q8×C89C2211yescharacteristic
33#106×C89C2214yes—
34C4×C8×C89C2211yescharacteristic
35#13083575—44no—
36C2×Dic178—21no—
37C2×Dic178—22no—
38Q8×D89—44no—
39C2×D356—22no—
40C2×D356—21no—
41C2×D356—21no—
42C2×D356C2312yes—
43C2×C4×D89—22no—
44C2×C4×D89—22no—
45C2×C4×D89D411yescharacteristic
46C2×C4×D89D411yescharacteristic
47C2×C4×D89C2311yescharacteristic
48C2×#10623494C2312yes—
49C4⋊Dic89—21no—
50C4⋊Dic89C2312yes—
51#13083553—22no—
52#13083553—22no—
53#13083551—22no—
54#13083551—22no—
55C4×Dic89D411yescharacteristic
56C4×Dic89D411yescharacteristic
57C4×Dic89C2311yescharacteristic
58C2×Q8×C89—21no—
59C2×Q8×C89—21no—
60C2×C8×C89C2312yes—
61C4⋊C4×C89—21no—
62C4⋊C4×C89—21no—
63C4⋊C4×C89C2312yes—
64C4⋊C4×C89C2312yes—
65C42×C89C2311yescharacteristic
66C22×D89—22no—
67C22×D89C2×D411yescharacteristic
68Q8×C89—42no—
69Q8×C89—42no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89C2×D411yescharacteristic
73C2×C4×C89C2×D411yescharacteristic
74C2×C4×C89C2411yescharacteristic
75C2×Dic89—22no—
76C2×Dic89C2×D411yescharacteristic
77C2×Dic89C2×D411yescharacteristic
78C2×Dic89C2×D411yescharacteristic
79D356—24no—
80D356—44no—
81D356—42no—
82D356—42no—
83C4×D89—22no—
84C4×D89—22no—
85C4×D89—44no—
86C4×D89—44no—
87C4×D89SD1614yes—
88Dic178—44no—
89Dic178—42no—
90C8×C89—22no—
91#10623494—22no—
92C22×C89C22×D411yescharacteristic
93C2×D89—21no—
94C2×D89—21no—
95C2×D89—42no—
96C2×D89—42no—
97C2×D89—42no—
98C2×D89C2×SD1612yes—
99C4×C89—42no—
100C4×C89—42no—
101C4×C89C2×SD1612yes—
102C4×C89AGL(1,ℤ/8)12yes—
103C4×C892−1+412yes—
104Dic89—21no—
105Dic89—21no—
106Dic89—42no—
107Dic89C2×SD1612yes—
108C2×C89#53611yescharacteristic
109C2×C89C22×SD1611yescharacteristic
110C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
111D89—22no—
112D89—82no—
113#3227—891nomaximal, Sylow
114C89#322711yescharacteristic, complemented, Sylow
115#532—891no—
116C2×C4⋊Q8—891no—
117#498—891no—
118#498D8911yescharacteristic, complemented
119#486—891no—
120#486—891no—
121#481—894no—
122#476—894no—
123#431—891no—
124C2×#41—1781no—
125C22×Q8—1781no—
126C4⋊Q8—892no—
127C4⋊Q8—891no—
128C4⋊Q8—1781no—
129C4⋊Q8—1781no—
130C4⋊Q8C2×D8911yescharacteristic
131C4⋊Q8C2×D8911yescharacteristic
132#127—891no—
133#124—1781no—
134#121—892no—
135#121—1781no—
136C4×D4—892no—
137C4×D4—1781no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—1781no—
140C2×C42—891no—
141#106—894no—
142#106C2×D8914yes—
143C4⋊C8—892no—
144#102—894no—
145#102—894no—
146C22⋊C8—892no—
147C4×C8—891no—
148C4×C8C2×D8911yescharacteristic
149#41—3564no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—3564no—
153C2×Q8—1782no—
154C2×Q8—1781no—
155C2×D4—892no—
156C2×D4—1782no—
157C2×D4—1781no—
158C2×D4—1781no—
159C22×C4—891no—
160C22×C4—891no—
161C22×C4—891no—
162C22×C4—1782no—
163C22×C4—1782no—
164C2×C8—892no—
165C2×C8C22×D8912yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—892no—
169C4⋊C4—1782no—
170C4⋊C4—1782no—
171C4⋊C4—1781no—
172C4⋊C4C22×D8912yes—
173C4⋊C4C22×D8912yes—
174C22⋊C4—1782no—
175C22⋊C4—1782no—
176C42—891no—
177C42—891no—
178C42—891no—
179C42C22×D8911yescharacteristic
180C23—891no—
181C23—1782no—
182Q8—42no—
183Q8—42no—
184Q8—3564no—
185Q8—3562no—
186D4—3564no—
187D4—3562no—
188D4—3562no—
189D4—1784no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—891no—
193C2×C4—894no—
194C2×C4—891no—
195C2×C4—891no—
196C2×C4—3564no—
197C2×C4—3564no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4D4×D8911yescharacteristic
202C2×C4D4×D8911yescharacteristic
203C2×C4C23×D8911yescharacteristic
204C8—22no—
205C8—1782no—
206C22—892no—
207C22—3562no—
208C22—3562no—
209C22—3562no—
210C22—1781no—
211C22—1781no—
212C22C2×D4×D8911yescharacteristic
213C4—42no—
214C4—42no—
215C4—892no—
216C4—3562no—
217C4—1781no—
218C4—1781no—
219C4SD16×D8912yes—
220C4#1566803912yes—
221C4#1566806012yes—
222C2—1782no—
223C2—7122no—
224C2#1915217311yescharacteristic
225C2C2×SD16×D8911yescharacteristic
226C2C2×#1566803911yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#498×C89C2
socleC22×C89C22×D4
prime radical#19152149C2
hypercenter#498D89
hypocenterC89#3227
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D89C2semidirect
3. #19151994C2semidirect
4. #19151946C2semidirect
5. #19151945C2semidirect
6. #19151918C2semidirect
7. #19151887C2semidirect
8. #19151649C2semidirect
9. #498×C89C2semidirect
114. C89#3227semidirect
118. #498D89semidirect

Maximal subgroups

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

subgroupindex
#191521492
C4⋊Q8×D892
#191519942
#191519462
#191519452
#191519182
#191518872
#191516492
#498×C892
#322789