Finite Group Databasebeta

← #26031397

Subgroups — #26031397

Order 11392.

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

normal subgroups only

This group has 360 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#19152153C211yesmaximal, characteristic
2C4⋊Q8×D89C211yesmaximal, characteristic
3#19151994C211yesmaximal, characteristic, complemented
4#19151950C211yesmaximal, characteristic, complemented
5#19151949C211yesmaximal, characteristic, complemented
6#19151930C214yesmaximal
7#19151882C214yesmaximal, complemented
8#19151649C211yesmaximal, characteristic
9#498×C89C211yesmaximal, characteristic, complemented
10C2×Q8×D89—21no—
11#15668012C2211yescharacteristic
12#15668012C2211yescharacteristic
13#15668011—21no—
14#15668011C2212yes—
15#15668010—21no—
16#15668003—21no—
17#15667992C2212yes—
18#15667988—21no—
19Q8×Dic89—21no—
20#15667977C2212yes—
21#15667970—21no—
22C4⋊C4×D89—21no—
23C4⋊C4×D89C2212yes—
24C42×D89C2211yescharacteristic
25#15667943C2214yes—
26#15667941C2212yes—
27#15667937C2214yes—
28#15667935C2214yes—
29#15667924C2212yes—
30C4×#10623494C2211yescharacteristic
31C4⋊Q8×C89C2211yescharacteristic
32C4⋊Q8×C89C2211yescharacteristic
33#106×C89C2214yes—
34C4×C8×C89C2211yescharacteristic
35C2×Dic178—21no—
36C2×Dic178—22no—
37C2×Dic178C2312yes—
38Q8×D89—44no—
39C2×C4×D89—22no—
40C2×C4×D89D411yescharacteristic
41C2×C4×D89D411yescharacteristic
42C2×C4×D89C2311yescharacteristic
43C2×#10623494C2312yes—
44C4⋊Dic89—21no—
45C4⋊Dic89—21no—
46C4⋊Dic89—21no—
47C4⋊Dic89—22no—
48C4⋊Dic89C2312yes—
49#13083553—22no—
50#13083553—22no—
51#13083553—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×D89C2×D411yescharacteristic
66Q8×C89—42no—
67Q8×C89—42no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89C2×D411yescharacteristic
71C2×C4×C89C2×D411yescharacteristic
72C2×C4×C89C2411yescharacteristic
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89C2×D411yescharacteristic
76C2×Dic89C2×D411yescharacteristic
77C2×Dic89C2×D411yescharacteristic
78C4×D89—22no—
79C4×D89—22no—
80C4×D89—44no—
81C4×D89SD1614yes—
82Dic178—24no—
83Dic178—42no—
84Dic178—44no—
85C8×C89—22no—
86#10623494—22no—
87C22×C89C22×D411yescharacteristic
88C2×D89—21no—
89C2×D89—21no—
90C2×D89C2×SD1612yes—
91C4×C89—42no—
92C4×C89—42no—
93C4×C89C2×SD1612yes—
94C4×C89#13712yes—
95C4×C892−1+412yes—
96Dic89—21no—
97Dic89—21no—
98Dic89—42no—
99Dic89—42no—
100Dic89C2×SD1612yes—
101C2×C89#53611yescharacteristic
102C2×C89C22×SD1611yescharacteristic
103C2×C89C2×#13711yescharacteristic
104D89—22no—
105#3229—891nomaximal, Sylow
106C89#322911yescharacteristic, complemented, Sylow
107#533—891no—
108C2×C4⋊Q8—891no—
109#498—891no—
110#498D8911yescharacteristic, complemented
111#487—891no—
112#487—891no—
113#483—894no—
114#475—894no—
115#431—891no—
116C22×Q8—1781no—
117C4⋊Q8—892no—
118C4⋊Q8—891no—
119C4⋊Q8—891no—
120C4⋊Q8—1781no—
121C4⋊Q8—1781no—
122C4⋊Q8C2×D8911yescharacteristic
123C4⋊Q8C2×D8911yescharacteristic
124#125—1781no—
125C22⋊Q8—892no—
126C22⋊Q8—1781no—
127C4×Q8—892no—
128C4×Q8—1781no—
129#117—1781no—
130C2×C4⋊C4—892no—
131C2×C4⋊C4—1781no—
132C2×C42—891no—
133#106—894no—
134#106C2×D8914yes—
135C4⋊C8—892no—
136#103—894no—
137#103—894no—
138C22⋊C8—892no—
139C4×C8—891no—
140C4×C8C2×D8911yescharacteristic
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—892no—
144C2×Q8—3564no—
145C2×Q8—1782no—
146C2×Q8—1781no—
147C22×C4—891no—
148C22×C4—891no—
149C22×C4—891no—
150C22×C4—1782no—
151C2×C8—892no—
152C2×C8C22×D8912yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—892no—
156C4⋊C4—1782no—
157C4⋊C4—1782no—
158C4⋊C4—1782no—
159C4⋊C4—1782no—
160C4⋊C4—1781no—
161C4⋊C4—1781no—
162C4⋊C4—1781no—
163C4⋊C4C22×D8912yes—
164C4⋊C4C22×D8912yes—
165C22⋊C4—1782no—
166C42—891no—
167C42—891no—
168C42—891no—
169C42—1782no—
170C42C22×D8911yescharacteristic
171C23—891no—
172Q8—42no—
173Q8—42no—
174Q8—3564no—
175Q8—3562no—
176Q8—1784no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—891no—
180C2×C4—894no—
181C2×C4—891no—
182C2×C4—891no—
183C2×C4—3564no—
184C2×C4—1782no—
185C2×C4—1782no—
186C2×C4—1782no—
187C2×C4—1782no—
188C2×C4D4×D8911yescharacteristic
189C2×C4D4×D8911yescharacteristic
190C2×C4C23×D8911yescharacteristic
191C8—22no—
192C8—1782no—
193C22—892no—
194C22—1781no—
195C22—1781no—
196C22C2×D4×D8911yescharacteristic
197C4—42no—
198C4—42no—
199C4—892no—
200C4—3562no—
201C4—3562no—
202C4—1781no—
203C4—1781no—
204C4SD16×D8912yes—
205C4#1566804112yes—
206C4#1566806012yes—
207C2—1782no—
208C2#1915217311yescharacteristic
209C2C2×SD16×D8911yescharacteristic
210C2C2×#1566804111yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#498×C89C2
socleC22×C89C22×D4
prime radicalC22×D89C2×D4
hypercenter#498D89
hypocenterC89#3229
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
3. #19151994C2semidirect
4. #19151950C2semidirect
5. #19151949C2semidirect
7. #19151882C2semidirect
9. #498×C89C2semidirect
106. C89#3229semidirect
110. #498D89semidirect

Maximal subgroups

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

subgroupindex
#191521532
C4⋊Q8×D892
#191519942
#191519502
#191519492
#191519302
#191518822
#191516492
#498×C892
#322989