Finite Group Databasebeta

← #26031337

Subgroups — #26031337

Order 11392.

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

normal subgroups only

This group has 364 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#19152210C211yesmaximal, characteristic, complemented
2#19152174C211yesmaximal, characteristic
3#19151992C211yesmaximal, characteristic, complemented
4#19151978C211yesmaximal, characteristic, complemented
5#19151967C211yesmaximal, characteristic, complemented
6#19151953C211yesmaximal, characteristic, complemented
7#19151821C212yesmaximal, complemented
8#19151809C212yesmaximal, complemented
9#19151762C212yesmaximal
10#19151756C212yesmaximal, complemented
11#433×C89C211yesmaximal, characteristic, complemented
12C2×#13083574C2211yescharacteristic
13C22×Dic178C2211yescharacteristic
14C2×Dic356C2212yes—
15C2×Dic356C2212yes—
16C2×Dic356C2212yes—
17C2×#13083563C2212yes—
18#15668012C2211yescharacteristic
19#15668012C2211yescharacteristic
20#15668012C2211yescharacteristic
21#15668005—22no—
22#15668004C2211yescharacteristic
23#15668002—22no—
24#15668000C2211yescharacteristic
25#15668000C2211yescharacteristic
26#15667996—22no—
27#15667992—22no—
28#15667991C2212yes—
29C4×Dic178C2212yes—
30#15667937C2212yes—
31#15667937C2212yes—
32#15667937C2212yes—
33#15667934C2212yes—
34#117×C89C2211yescharacteristic
35C4⋊C8×C89C2212yes—
36C22⋊C8×C89C2212yes—
37#97×C89C2211yescharacteristic
38C4×C8×C89C2211yescharacteristic
39#13083574—42no—
40C2×Dic178—21no—
41C2×Dic178—42no—
42C2×Dic178C2312yes—
43C2×Dic178C2311yescharacteristic
44C2×Dic178C2311yescharacteristic
45C2×Dic178C2311yescharacteristic
46C2×D356C2311yescharacteristic
47C2×C22⋊D89—21no—
48C22×Dic89—21no—
49C2×C4×D89—21no—
50Dic356—42no—
51Dic356—42no—
52Dic356—42no—
53#13083563—42no—
54C4⋊Dic89—22no—
55C4⋊Dic89—22no—
56C4⋊Dic89—22no—
57C4⋊Dic89C2312yes—
58#13083553—22no—
59#13083553—22no—
60#13083553—22no—
61C22⋊Dic89—22no—
62#13083551—22no—
63#13083551—22no—
64C4×Dic89—22no—
65C22×C4×C89C2311yescharacteristic
66C2×C8×C89C2312yes—
67C2×C8×C89C2312yes—
68C4⋊C4×C89D412yes—
69C22⋊C4×C89D412yes—
70C42×C89C2311yescharacteristic
71C42×C89C2311yescharacteristic
72C23×C89C2×D411yescharacteristic
73C22×D89—21no—
74C2×C4×C89—22no—
75C2×C4×C89C2×D412yes—
76C2×C4×C89C2×D412yes—
77C2×C4×C89C2×D411yescharacteristic
78C2×C4×C89C2411yescharacteristic
79C22⋊D89—42no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—21no—
83C2×Dic89—21no—
84C2×Dic89—21no—
85C2×Dic89—42no—
86D356—22no—
87C4×D89—42no—
88Dic178—22no—
89Dic178—22no—
90Dic178—22no—
91Dic178—22no—
92Dic178—22no—
93Dic178—42no—
94C8×C89—22no—
95C8×C89—22no—
96C22×C89—21no—
97C22×C89—22no—
98C22×C89C22×D411yescharacteristic
99C2×D89—41no—
100C2×D89—42no—
101C4×C89—21no—
102C4×C89—22no—
103C4×C89—22no—
104C4×C89H(5,𝔽2)12yes—
105Dic89—41no—
106Dic89—41no—
107Dic89—41no—
108Dic89—42no—
109Dic89—42no—
110C2×C89—41no—
111C2×C89#53511yescharacteristic
112C2×C89#57812yes—
113D89—81no—
114#3223—891nomaximal, Sylow
115C89#322311yescharacteristic, complemented, Sylow
116#541—891no—
117#536—891no—
118#497—891no—
119#494—891no—
120#491—891no—
121#488—891no—
122#464—892no—
123#462—892no—
124#452—892no—
125#451—892no—
126#433D8911yescharacteristic, complemented
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—891no—
138#125—1782no—
139#124—891no—
140#124—891no—
141#123—1782no—
142C22⋊Q8—892no—
143C22⋊Q8—1782no—
144C4×Q8—892no—
145#117C2×D8911yescharacteristic
146C4⋊C8C2×D8912yes—
147#103—892no—
148#103—892no—
149#103—892no—
150#102—892no—
151C22⋊C8C2×D8912yes—
152#97C2×D8911yescharacteristic
153C4×C8C2×D8911yescharacteristic
154#41—3562no—
155C2×Q8—891no—
156C2×Q8—891no—
157C2×Q8—891no—
158C2×Q8—892no—
159C2×Q8—3562no—
160C2×Q8—1781no—
161C2×D4—891no—
162C2×D4—1781no—
163C22×C4—1781no—
164C22×C4—1781no—
165C22×C4C22×D8911yescharacteristic
166Q16—3562no—
167Q16—3562no—
168Q16—3562no—
169SD16—3562no—
170C2×C8C22×D8912yes—
171C2×C8C22×D8912yes—
172C4⋊C4—892no—
173C4⋊C4—1782no—
174C4⋊C4—1782no—
175C4⋊C4—1782no—
176C4⋊C4—1782no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4D35612yes—
180C22⋊C4—1782no—
181C22⋊C4—1782no—
182C22⋊C4—1782no—
183C22⋊C4D35612yes—
184C42—1782no—
185C42C22×D8911yescharacteristic
186C42C22×D8911yescharacteristic
187C23—1781no—
188C23C2×D35611yescharacteristic
189Q8—3562no—
190Q8—1782no—
191Q8—1782no—
192Q8—1782no—
193Q8—1782no—
194Q8—1782no—
195D4—3562no—
196D4—1782no—
197C2×C4—22no—
198C2×C4—3562no—
199C2×C4—3562no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1781no—
203C2×C4—1781no—
204C2×C4—1781no—
205C2×C4C2×D35612yes—
206C2×C4C2×D35612yes—
207C2×C4C2×D35611yescharacteristic
208C2×C4C23×D8911yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—3562no—
214C22—3561no—
215C22C22×D35611yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—3562no—
220C4—3561no—
221C4—3561no—
222C4—3561no—
223C4—3562no—
224C4#1566805812yes—
225C2—41no—
226C2—7121no—
227C2#1915216711yescharacteristic
228C2#1915241512yes—
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#433×C89C2
socleC22×C89C22×D4
prime radicalC2×#13083574C22
hypercenter#433D89
hypocenterC89#3223
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19152210C2semidirect
3. #19151992C2semidirect
4. #19151978C2semidirect
5. #19151967C2semidirect
6. #19151953C2semidirect
7. #19151821C2semidirect
8. #19151809C2semidirect
10. #19151756C2semidirect
11. #433×C89C2semidirect
115. C89#3223semidirect
126. #433D89semidirect

Maximal subgroups

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

subgroupindex
#191522102
#191521742
#191519922
#191519782
#191519672
#191519532
#191518212
#191518092
#191517622
#191517562
#433×C892
#322389