Finite Group Databasebeta

← #26031330

Subgroups — #26031330

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#19152209C211yesmaximal, characteristic, complemented
2#19152168C211yesmaximal, characteristic
3#19151977C211yesmaximal, characteristic, complemented
4#19151967C211yesmaximal, characteristic, complemented
5#19151952C211yesmaximal, characteristic, complemented
6#19151818C212yesmaximal, complemented
7#19151806C212yesmaximal, complemented
8#19151757C212yesmaximal
9#19151752C212yesmaximal, complemented
10#19151660C211yesmaximal, characteristic, complemented
11#497×C89C211yesmaximal, characteristic, complemented
12C2×#13083573C2211yescharacteristic
13C2×Q8×D89C2211yescharacteristic
14C2×#13083564C2212yes—
15C2×#13083564C2212yes—
16#15668012C2211yescharacteristic
17#15668010C2211yescharacteristic
18#15668007—22no—
19#15668004C2211yescharacteristic
20#15668002—22no—
21#15667999C2211yescharacteristic
22#15667994—22no—
23#15667989—22no—
24#15667988C2212yes—
25Q8×Dic89C2212yes—
26#15667969C2211yescharacteristic
27#15667941C2212yes—
28#15667937C2212yes—
29#15667937C2212yes—
30#15667936C2212yes—
31#15667933C2212yes—
32#15667924C2212yes—
33C4×#10623494C2211yescharacteristic
34C2×Q16×C89C2212yes—
35C2×SD16×C89C2212yes—
36C4⋊Q8×C89C2211yescharacteristic
37#124×C89C2211yescharacteristic
38#97×C89C2211yescharacteristic
39#13083573—42no—
40C2×Dic178—21no—
41C2×Dic178C2311yescharacteristic
42C2×Dic178C2311yescharacteristic
43Q8×D89—42no—
44C2×C22⋊D89—21no—
45C22×Dic89—21no—
46C2×C4×D89—21no—
47C2×C4×D89C2311yescharacteristic
48#13083564—42no—
49#13083564—42no—
50C2×#10623494C2312yes—
51C4⋊Dic89—22no—
52C4⋊Dic89—22no—
53C4⋊Dic89C2312yes—
54#13083553—22no—
55#13083553—22no—
56#13083553—22no—
57#13083553D412yes—
58C22⋊Dic89—22no—
59#13083551—22no—
60#13083551D412yes—
61C4×Dic89—22no—
62C4×Dic89C2311yescharacteristic
63C2×Q8×C89C2312yes—
64C2×Q8×C89C2311yescharacteristic
65C2×D4×C89C2311yescharacteristic
66Q16×C89—42no—
67SD16×C89—42no—
68C2×C8×C89C2312yes—
69C4⋊C4×C89—22no—
70C22⋊C4×C89—22no—
71C42×C89C2311yescharacteristic
72C23×C89—21no—
73C22×D89C2×D411yescharacteristic
74Q8×C89—22no—
75Q8×C89—22no—
76Q8×C89—22no—
77D4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—22no—
80C2×C4×C89C2×D412yes—
81C2×C4×C89C2411yescharacteristic
82C22⋊D89—42no—
83C2×Dic89—22no—
84C2×Dic89—21no—
85C2×Dic89—21no—
86C2×Dic89—42no—
87C2×Dic89C2×D412yes—
88C2×Dic89C2×D411yescharacteristic
89C4×D89—22no—
90C4×D89—42no—
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—41no—
109Dic89—42no—
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#497D8911yescharacteristic, complemented
119#494—891no—
120#491—891no—
121#488—891no—
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×Q16C2×D8912yes—
132C2×SD16C2×D8912yes—
133C4⋊Q8—891no—
134C4⋊Q8—891no—
135C4⋊Q8C2×D8911yescharacteristic
136#126—1782no—
137#125—891no—
138#125—1782no—
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#103—892no—
150#102—892no—
151C22⋊C8—892no—
152#97C2×D8911yescharacteristic
153C4×C8—891no—
154#41—3562no—
155C2×Q8—891no—
156C2×Q8—891no—
157C2×Q8—3562no—
158C2×Q8—1781no—
159C2×Q8C22×D8911yescharacteristic
160C2×Q8C22×D8912yes—
161C2×D4—1781no—
162C2×D4C22×D8911yescharacteristic
163C22×C4—891no—
164C22×C4—1781no—
165C22×C4—1781no—
166Q16—42no—
167Q16—3562no—
168Q16—3562no—
169SD16—42no—
170C2×C8—892no—
171C2×C8C22×D8912yes—
172C4⋊C4—22no—
173C4⋊C4—892no—
174C4⋊C4—892no—
175C4⋊C4—1782no—
176C4⋊C4—1782no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4—1782no—
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—22no—
191Q8—22no—
192Q8—3562no—
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—41no—
218C4—42no—
219C4—3562no—
220C4—3561no—
221C4—3561no—
222C4—1782no—
223C4—1781no—
224C4#1566805712yes—
225C2—81no—
226C2—3561no—
227C2#1915216111yescharacteristic
228C2#1915241412yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#497×C89C2
socleC22×C89C22×D4
prime radicalC2×#13083573C22
hypercenter#497D89
hypocenterC89#3223
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #19152209C2semidirect
3. #19151977C2semidirect
4. #19151967C2semidirect
5. #19151952C2semidirect
6. #19151818C2semidirect
7. #19151806C2semidirect
9. #19151752C2semidirect
10. #19151660C2semidirect
11. #497×C89C2semidirect
115. C89#3223semidirect
118. #497D89semidirect

Maximal subgroups

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

subgroupindex
#191522092
#191521682
#191519772
#191519672
#191519522
#191518182
#191518062
#191517572
#191517522
#191516602
#497×C892
#322389