Finite Group Databasebeta

← C22×#15667987 #26033475

Subgroups — C22×#15667987 #26033475

Order 11392.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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
1C23×D356C212yesmaximal, complemented
2C23×D356C211yesmaximal, characteristic, complemented
3C23×C4×D89C211yesmaximal, characteristic, complemented
4C2×#15667987C2124yesmaximal, direct product factor
5C22×#13083551C212yesmaximal, complemented
6C22×C4⋊C4×C89C211yesmaximal, characteristic, complemented
7C24×D89C2212yes—
8C24×D89C2211yescharacteristic
9C22×D356—216no—
10C22×D356—28no—
11C22×D356C22124yescomplemented
12C22×D356C22112yescomplemented
13C23×Dic89C2211yescharacteristic
14C22×C4×D89—28no—
15C22×C4×D89C22112yescomplemented
16#15667987C22164yesdirect product factor
17C2×#13083551C22124yescomplemented
18C23×C4×C89C2212yes—
19C23×C4×C89C2211yescharacteristic
20C2×C4⋊C4×C89C22112yescomplemented
21C23×D89—24no—
22C23×D89—24no—
23C23×D89—28no—
24C23×D89—28no—
25C23×D89—28no—
26C23×D89D418yescomplemented
27C23×D89C23112yes—
28C23×D89C2316yes—
29C2×D356—296no—
30C2×D356—248no—
31C2×D356C23132yescomplemented
32C2×D356C23116yescomplemented
33C22×Dic89—24no—
34C22×Dic89C2316yes—
35C2×C4×D89—248no—
36C2×C4×D89C23116yescomplemented
37#13083551C23132yescomplemented
38C24×C89C2311yescharacteristic
39C22×C4×C89—28no—
40C22×C4×C89D418yescomplemented
41C22×C4×C89C23112yes—
42C22×C4×C89C2316yes—
43C4⋊C4×C89C23116yescomplemented
44C23×C89C2×D414yes—
45C23×C89C2×D414yes—
46C23×C89#4114yes—
47C23×C89C2413yes—
48C22×D89—232no—
49C22×D89—212no—
50C22×D89—212no—
51C22×D89—224no—
52C22×D89—224no—
53C22×D89—224no—
54C22×D89—432no—
55C22×D89C2×D4124yescomplemented
56C22×D89C2418yes—
57C22×D89C2414yes—
58C2×C4×C89—224no—
59C2×C4×C89C2×D4124yescomplemented
60C2×C4×C89C2418yes—
61C2×C4×C89C2414yes—
62C2×Dic89—212no—
63C2×Dic89C2414yes—
64D356—264no—
65D356—232no—
66C4×D89—232no—
67C22×C89#121116yescomplemented
68C22×C89C22×D416yes—
69C22×C89C22×D416yes—
70C22×C89C2×#4116yes—
71C22×C89C2511yescharacteristic
72C2×D89—248no—
73C2×D89—24no—
74C2×D89—24no—
75C2×D89—28no—
76C2×D89—28no—
77C2×D89—28no—
78C2×D89—448no—
79C2×D89C22×D418yescomplemented
80C4×C89—28no—
81C4×C89C22×D418yescomplemented
82Dic89—24no—
83C2×C89C2×#121112yescomplemented
84C2×C89C23×D411yescharacteristic
85C2×C89C23×D411yescharacteristic
86C2×C89C22×#4111yescharacteristic
87D89—28no—
88D89—48no—
89C22×#121—891nomaximal, Sylow
90C89C22×#12111yescharacteristic, complemented, Sylow
91C23×D4—892no—
92C23×D4—891no—
93C24×C4—891no—
94C2×#121—8924no—
95C22×C4⋊C4D8911yescharacteristic, complemented
96C22×C22⋊C4—892no—
97C25—891no—
98C25—892no—
99C22×D4—8924no—
100C22×D4—8912no—
101C22×D4—17816no—
102C22×D4—1788no—
103C23×C4—891no—
104C23×C4—8912no—
105C23×C4—1788no—
106C23×C4C2×D8912yes—
107C23×C4C2×D8911yescharacteristic
108#121—8964no—
109C2×C4⋊C4C2×D89112yescomplemented
110C2×C22⋊C4—8924no—
111C24—898no—
112C24—896no—
113C24—8912no—
114C24—1788no—
115C24—1788no—
116C24—1788no—
117C24—1784no—
118C24—1784no—
119C24C22×D8911yescharacteristic
120C2×D4—8932no—
121C2×D4—8916no—
122C2×D4—17896no—
123C2×D4—17848no—
124C22×C4—28no—
125C22×C4—896no—
126C22×C4—8916no—
127C22×C4—1784no—
128C22×C4—17848no—
129C22×C4D35618yescomplemented
130C22×C4C22×D89112yes—
131C22×C4C22×D8916yes—
132C4⋊C4C22×D89116yescomplemented
133C22⋊C4—8932no—
134C23—8924no—
135C23—894no—
136C23—898no—
137C23—35632no—
138C23—17824no—
139C23—17824no—
140C23—17824no—
141C23—17832no—
142C23—17812no—
143C23—17812no—
144C23D4×D8914yes—
145C23C2×D35614yes—
146C23#1308357514yes—
147C23C23×D8913yes—
148D4—17864no—
149D4—17832no—
150C2×C4—224no—
151C2×C4—894no—
152C2×C4—17812no—
153C2×C4—17832no—
154C2×C4C2×D356124yescomplemented
155C2×C4C23×D8918yes—
156C2×C4C23×D8914yes—
157C22—898no—
158C22—35648no—
159C22—1788no—
160C22—1788no—
161C22—1788no—
162C22—1784no—
163C22—1784no—
164C22—17848no—
165C22#15667987116yesdirect product factor
166C22C2×D4×D8916yes—
167C22C22×D35616yes—
168C22C2×#1308357516yes—
169C22C24×D8911yescharacteristic
170C4—28no—
171C4—1784no—
172C4C22×D35618yescomplemented
173C2—3568no—
174C2—1788no—
175C2C2×#15667987112yesdirect product factor
176C2C22×D4×D8911yescharacteristic
177C2C23×D35611yescharacteristic
178C2C22×#1308357511yescharacteristic
subgroupG/H
centerC24C22×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC22×C4⋊C4×C89C2
socleC24×C89C23
hypercenterC22×C4⋊C4D89
hypocenterC89C22×#121
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D356C2semidirect
2. C23×D356C2semidirect
3. C23×C4×D89C2semidirect
4. C2×#15667987C2direct (N × H)
5. C22×#13083551C2semidirect
6. C22×C4⋊C4×C89C2semidirect
11. C22×D356C22semidirect
12. C22×D356C22semidirect
15. C22×C4×D89C22semidirect
16. #15667987C22direct (N × H)
17. C2×#13083551C22semidirect
20. C2×C4⋊C4×C89C22semidirect
26. C23×D89D4semidirect
31. C2×D356C23semidirect
32. C2×D356C23semidirect
36. C2×C4×D89C23semidirect
37. #13083551C23semidirect
40. C22×C4×C89D4semidirect
43. C4⋊C4×C89C23semidirect
55. C22×D89C2×D4semidirect
59. C2×C4×C89C2×D4semidirect
67. C22×C89#121semidirect
79. C2×D89C22×D4semidirect
81. C4×C89C22×D4semidirect
83. C2×C89C2×#121semidirect
90. C89C22×#121semidirect
95. C22×C4⋊C4D89semidirect
109. C2×C4⋊C4C2×D89semidirect
129. C22×C4D356semidirect
132. C4⋊C4C22×D89semidirect
154. C2×C4C2×D356semidirect
165. C22#15667987direct (N × H)
172. C4C22×D356semidirect
175. C2C2×#15667987direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3562
C23×C4×D892
C2×#156679872
C22×#130835512
C22×C4⋊C4×C892
C22×#12189