Finite Group Databasebeta

← #26031338

Subgroups — #26031338

Order 11392.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#19152211C211yesmaximal, characteristic, complemented
2#19152168C211yesmaximal, characteristic
3#19151993C211yesmaximal, characteristic, complemented
4#19151978C211yesmaximal, characteristic, complemented
5#19151968C211yesmaximal, characteristic, complemented
6#19151819C212yesmaximal, complemented
7#19151807C212yesmaximal, complemented
8#19151761C212yesmaximal
9#19151755C212yesmaximal, complemented
10#19151657C211yesmaximal, characteristic, complemented
11#488×C89C211yesmaximal, characteristic, complemented
12C2×#13083573C2211yescharacteristic
13C2×Q8×D89C2211yescharacteristic
14C2×Dic356C2212yes—
15C2×Dic356C2212yes—
16C2×#13083564C2212yes—
17C2×#13083562C2212yes—
18#15668012C2211yescharacteristic
19#15668012C2211yescharacteristic
20#15668010C2211yescharacteristic
21#15668007—22no—
22#15668003—22no—
23#15667999C2211yescharacteristic
24#15667994—22no—
25#15667992C2212yes—
26#15667989—22no—
27#15667977C2212yes—
28#15667969C2211yescharacteristic
29#15667941C2212yes—
30#15667935C2212yes—
31#15667935C2212yes—
32#15667924C2212yes—
33#15667923C2211yescharacteristic
34#125×C89C2211yescharacteristic
35#124×C89C2211yescharacteristic
36#103×C89C2212yes—
37#102×C89C2212yes—
38C4×C8×C89C2211yescharacteristic
39#13083573—42no—
40C2×Dic178—21no—
41C2×Dic178C2312yes—
42C2×Dic178C2311yescharacteristic
43C2×Dic178C2311yescharacteristic
44Q8×D89—42no—
45C2×C22⋊D89—21no—
46C22×Dic89—21no—
47C2×C4×D89—21no—
48C2×C4×D89C2311yescharacteristic
49Dic356—42no—
50Dic356—42no—
51#13083564—42no—
52#13083562—42no—
53C2×#10623494C2312yes—
54C4⋊Dic89—22no—
55C4⋊Dic89—22no—
56C4⋊Dic89—22no—
57#13083553—22no—
58#13083553—22no—
59#13083553D412yes—
60C22⋊Dic89—22no—
61#13083551—22no—
62#13083551D412yes—
63C4×Dic89—22no—
64C4×Dic89C2311yescharacteristic
65C2×Q8×C89C2311yescharacteristic
66C2×D4×C89C2311yescharacteristic
67C2×C8×C89C2312yes—
68C4⋊C4×C89—22no—
69C4⋊C4×C89C2312yes—
70C22⋊C4×C89—22no—
71C42×C89C2311yescharacteristic
72C23×C89—21no—
73C22×D89C2×D411yescharacteristic
74Q8×C89—22no—
75D4×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89C2×D412yes—
79C2×C4×C89C2411yescharacteristic
80C22⋊D89—42no—
81C2×Dic89—22no—
82C2×Dic89—21no—
83C2×Dic89—21no—
84C2×Dic89—42no—
85C2×Dic89C2×D412yes—
86C2×Dic89C2×D411yescharacteristic
87C4×D89—22no—
88C4×D89—42no—
89Dic178—22no—
90Dic178—22no—
91Dic178—22no—
92Dic178—22no—
93Dic178—42no—
94C8×C89—22no—
95#10623494—22no—
96C22×C89—41no—
97C22×C89—42no—
98C22×C89C22×D411yescharacteristic
99C2×D89—21no—
100C2×D89—22no—
101C4×C89—22no—
102C4×C89—41no—
103C4×C89—42no—
104C4×C89H(5,𝔽2)12yes—
105Dic89—21no—
106Dic89—22no—
107Dic89—41no—
108Dic89—42no—
109Dic89—41no—
110C2×C89—81no—
111C2×C89#53511yescharacteristic
112C2×C89#57812yes—
113D89—41no—
114#3223—891nomaximal, Sylow
115C89#322311yescharacteristic, complemented, Sylow
116#541—891no—
117#536—891no—
118#497—891no—
119#494—891no—
120#491—891no—
121#488D8911yescharacteristic, complemented
122#464—892no—
123#462—892no—
124#452—892no—
125#451—892no—
126#433—891no—
127C2×#41—891no—
128C22×Q8—891no—
129C2×Q16—892no—
130C2×Q16—892no—
131C2×Q16—892no—
132C2×SD16—892no—
133C4⋊Q8—891no—
134C4⋊Q8—891no—
135C4⋊Q8—891no—
136#126—1782no—
137#125—1782no—
138#125C2×D8911yescharacteristic
139#124—891no—
140#124C2×D8911yescharacteristic
141#123—1782no—
142C22⋊Q8—892no—
143C22⋊Q8—1782no—
144C4×Q8—892no—
145#117—891no—
146C4⋊C8—892no—
147#103—892no—
148#103—892no—
149#103C2×D8912yes—
150#102C2×D8912yes—
151C22⋊C8—892no—
152#97—891no—
153C4×C8C2×D8911yescharacteristic
154#41—3562no—
155C2×Q8—891no—
156C2×Q8—891no—
157C2×Q8—892no—
158C2×Q8—3562no—
159C2×Q8—1781no—
160C2×Q8C22×D8911yescharacteristic
161C2×D4—1781no—
162C2×D4C22×D8911yescharacteristic
163C22×C4—891no—
164C22×C4—1781no—
165C22×C4—1781no—
166Q16—3562no—
167Q16—3562no—
168Q16—3562no—
169SD16—3562no—
170C2×C8—892no—
171C2×C8C22×D8912yes—
172C4⋊C4—22no—
173C4⋊C4—892no—
174C4⋊C4—1782no—
175C4⋊C4—1782no—
176C4⋊C4—1782no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4C22×D8912yes—
180C22⋊C4—22no—
181C22⋊C4—892no—
182C22⋊C4—1782no—
183C22⋊C4—1782no—
184C42—891no—
185C42—1782no—
186C42C22×D8911yescharacteristic
187C23—21no—
188C23—891no—
189Q8—22no—
190Q8—3562no—
191Q8—1782no—
192Q8—1782no—
193Q8—1782no—
194Q8—1782no—
195D4—22no—
196D4—3562no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—892no—
200C2×C4—891no—
201C2×C4—3562no—
202C2×C4—3562no—
203C2×C4—1782no—
204C2×C4—1781no—
205C2×C4—1781no—
206C2×C4—1782no—
207C2×C4D4×D8912yes—
208C2×C4C23×D8911yescharacteristic
209C8—22no—
210C8—1782no—
211C22—42no—
212C22—41no—
213C22—1782no—
214C22—1781no—
215C22C2×D4×D8911yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—3561no—
220C4—3561no—
221C4—3562no—
222C4—1782no—
223C4—1781no—
224C4#1566805812yes—
225C2—81no—
226C2—3561no—
227C2#1915216611yescharacteristic
228C2#1915241212yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#488×C89C2
socleC22×C89C22×D4
prime radicalC2×#13083573C22
hypercenter#488D89
hypocenterC89#3223
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #19152211C2semidirect
3. #19151993C2semidirect
4. #19151978C2semidirect
5. #19151968C2semidirect
6. #19151819C2semidirect
7. #19151807C2semidirect
9. #19151755C2semidirect
10. #19151657C2semidirect
11. #488×C89C2semidirect
115. C89#3223semidirect
121. #488D89semidirect

Maximal subgroups

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

subgroupindex
#191522112
#191521682
#191519932
#191519782
#191519682
#191518192
#191518072
#191517612
#191517552
#191516572
#488×C892
#322389