Finite Group Databasebeta

← #26033664

Subgroups — #26033664

Order 11392.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#19152197C216yesmaximal, complemented
2#19152188C216yesmaximal, complemented
3#19152160C213yesmaximal, complemented
4#19152134C216yesmaximal, complemented
5#19152111C216yesmaximal, complemented
6C2×#15667972C213yesmaximal, complemented
7#543×C89C211yesmaximal, characteristic, complemented
8C2×#13083575C2212yescomplemented
9C22×C22⋊D89C2213yes—
10C23×Dic89C2211yescharacteristic
11C22×C4×D89C2213yescomplemented
12#15668007C22112yescomplemented
13#15668003C2216yescomplemented
14#15668001C2216yescomplemented
15#15667997C22112yescomplemented
16#15667996C22112yescomplemented
17#15667988C2216yescomplemented
18#15667987C2216yescomplemented
19#15667986C2216yes—
20#15667986C2216yes—
21#15667982C22112yescomplemented
22Q8×Dic89C2212yescomplemented
23#15667974C2216yescomplemented
24#15667972C22112yescomplemented
25#15667972C22112yescomplemented
26#15667970C2216yescomplemented
27C2×#13083553C2213yescomplemented
28C2×#13083551C2213yescomplemented
29C2×C4×Dic89C2213yescomplemented
30C22⋊Q8×C89C2216yescomplemented
31C22⋊Q8×C89C2216yescomplemented
32C2×C22⋊C4×C89C2213yes—
33C23×D89C2313yes—
34#13083575—44no—
35C2×D356C2316yes—
36C2×D356C2316yes—
37C2×C22⋊D89—212no—
38C2×C22⋊D89C23112yes—
39C22×Dic89—42no—
40C22×Dic89C2313yes—
41C22×Dic89C2313yes—
42C22×Dic89C2313yes—
43C2×C4×D89—46no—
44C2×C4×D89C2316yes—
45C2×C4×D89C2316yes—
46C4⋊Dic89C2316yes—
47C4⋊Dic89C2316yes—
48#13083553C23112yes—
49#13083551C23112yes—
50#13083551C23112yes—
51#13083551C23112yes—
52C4×Dic89C2316yes—
53C4×Dic89C2316yes—
54C24×C89C2311yescharacteristic
55C2×Q8×C89C2312yes—
56C2×Q8×C89C2312yes—
57C22×C4×C89C2313yes—
58C22×C4×C89C2313yes—
59C4⋊C4×C89C2316yes—
60C4⋊C4×C89C2316yes—
61C22⋊C4×C89C23112yes—
62C23×C89—41no—
63C23×C89—41no—
64C23×C89#4114yescomplemented
65C23×C89C2413yes—
66C22×D89—26no—
67C22×D89—43no—
68C22×D89—43no—
69C22×D89C2416yes—
70Q8×C89—42no—
71Q8×C89—42no—
72C2×C4×C89—43no—
73C2×C4×C89—43no—
74C2×C4×C89C2416yes—
75C2×C4×C89C2416yes—
76C22⋊D89—224no—
77C2×Dic89—26no—
78C2×Dic89—26no—
79C2×Dic89—43no—
80C2×Dic89C2413yes—
81C2×Dic89C2416yes—
82C2×Dic89C2411yescharacteristic
83D356—46no—
84D356—46no—
85C4×D89—212no—
86C4×D89—46no—
87C22×C89—23no—
88C22×C89—23no—
89C22×C89—44no—
90C22×C89C2×#4116yes—
91C22×C89C2511yescharacteristic
92C2×D89—26no—
93C2×D89—26no—
94C2×D89—26no—
95C2×D89—412no—
96C4×C89—26no—
97C4×C89—26no—
98Dic89—26no—
99Dic89—23no—
100Dic89H(5,𝔽2)12yes—
101C2×C89—26no—
102C2×C89C22×#4111yescharacteristic
103C2×C89C2×H(5,𝔽2)11yescharacteristic
104C2×C89#58511yescharacteristic
105D89—46no—
106#3459—891nomaximal, Sylow
107C89#345911yescharacteristic, complemented, Sylow
108#543D8911yescharacteristic, complemented
109#539—896no—
110#538—896no—
111#534—893no—
112#529—896no—
113#525—896no—
114C2×C4×D4—893no—
115C2×#41—892no—
116C22×D4—893no—
117C23×C4—891no—
118C23×C4—893no—
119#126—8912no—
120#125—896no—
121#124—896no—
122#123—8912no—
123#123—8912no—
124C22⋊Q8—896no—
125C22⋊Q8C2×D8916yescomplemented
126C22⋊Q8C2×D8916yescomplemented
127#121—896no—
128#121—896no—
129#121—896no—
130#120—8912no—
131C4×Q8—892no—
132C4×D4—896no—
133C4×D4—8912no—
134C4×D4—8912no—
135#117—896no—
136C2×C4⋊C4—893no—
137C2×C22⋊C4—893no—
138C2×C22⋊C4C2×D8913yes—
139C2×C42—893no—
140C24—893no—
141C24C22×D8911yescharacteristic
142#41—3564no—
143C2×Q8C22×D8912yes—
144C2×Q8C22×D8912yes—
145C2×D4—8912no—
146C2×D4—896no—
147C2×D4—896no—
148C2×D4—17812no—
149C22×C4—893no—
150C22×C4—893no—
151C22×C4—893no—
152C22×C4—896no—
153C22×C4—896no—
154C22×C4—3566no—
155C22×C4—3562no—
156C22×C4C22×D8913yes—
157C22×C4C22×D8913yes—
158C4⋊C4—8912no—
159C4⋊C4—896no—
160C4⋊C4—896no—
161C4⋊C4C22×D8916yes—
162C4⋊C4C22×D8916yes—
163C22⋊C4—8912no—
164C22⋊C4—8912no—
165C22⋊C4—8912no—
166C22⋊C4C22×D89112yes—
167C42—896no—
168C42—896no—
169C23—41no—
170C23—41no—
171C23—896no—
172C23—3563no—
173C23—3563no—
174C23—1786no—
175C23#1308357514yescomplemented
176C23C23×D8913yes—
177Q8—42no—
178Q8—42no—
179D4—3566no—
180D4—3566no—
181D4—17824no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—891no—
185C2×C4—896no—
186C2×C4—893no—
187C2×C4—3566no—
188C2×C4—3563no—
189C2×C4—17812no—
190C2×C4—1786no—
191C2×C4—1786no—
192C2×C4C23×D8916yes—
193C2×C4C23×D8916yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—35612no—
198C22—1786no—
199C22—1786no—
200C22—1786no—
201C22C2×#1308357516yes—
202C22C24×D8911yescharacteristic
203C4—26no—
204C4—26no—
205C4—892no—
206C4—1786no—
207C4—1783no—
208C2—26no—
209C2—3566no—
210C2C22×#1308357511yescharacteristic
211C2H(5,𝔽2)×D8911yescharacteristic
212C2#1915243311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D89
commutator, socle, cosocleC22×C89C25
Fitting#543×C89C2
hypercenter#543D89
hypocenterC89#3459
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #19152197C2semidirect
2. #19152188C2semidirect
3. #19152160C2semidirect
4. #19152134C2semidirect
5. #19152111C2semidirect
6. C2×#15667972C2semidirect
7. #543×C89C2semidirect
8. C2×#13083575C22semidirect
11. C22×C4×D89C22semidirect
12. #15668007C22semidirect
13. #15668003C22semidirect
14. #15668001C22semidirect
15. #15667997C22semidirect
16. #15667996C22semidirect
17. #15667988C22semidirect
18. #15667987C22semidirect
21. #15667982C22semidirect
22. Q8×Dic89C22semidirect
23. #15667974C22semidirect
24. #15667972C22semidirect
25. #15667972C22semidirect
26. #15667970C22semidirect
27. C2×#13083553C22semidirect
28. C2×#13083551C22semidirect
29. C2×C4×Dic89C22semidirect
30. C22⋊Q8×C89C22semidirect
31. C22⋊Q8×C89C22semidirect
64. C23×C89#41semidirect
107. C89#3459semidirect
108. #543D89semidirect
125. C22⋊Q8C2×D89semidirect
126. C22⋊Q8C2×D89semidirect
175. C23#13083575semidirect

Maximal subgroups

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

subgroupindex
#191521972
#191521882
#191521602
#191521342
#191521112
C2×#156679722
#543×C892
#345989