Finite Group Databasebeta

← #31826973

Subgroups — #31826973

Order 18112.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#17985391C211yesmaximal, characteristic, complemented
2C22×C4×D283C211yesmaximal, characteristic, complemented
3#22583593C211yesmaximal, characteristic, complemented
4#22583588C212yesmaximal, complemented
5#22583583C212yesmaximal, complemented
6#22583580C211yesmaximal, characteristic, complemented
7#22583578C211yesmaximal, characteristic, complemented
8#22583572C212yesmaximal, complemented
9(C22⋊D283)⋊C4C212yesmaximal, complemented
10#22583566C211yesmaximal, characteristic, complemented
11#123×C283C211yesmaximal, characteristic, complemented
12C23×D283C2211yescharacteristic
13#17985391—24no—
14C2×Dic566C2211yescharacteristic, complemented
15C2×D1132C2212yes—
16C2×C22⋊D283C2212yes—
17C2×C22⋊D283C2211yescharacteristic
18C2×C22⋊D283C2211yescharacteristic, complemented
19C22×Dic283C2211yescharacteristic
20C22×Dic283C2211yescharacteristic, complemented
21C2×C4×D283—24no—
22C2×C4×D283C2212yes—
23C2×C4×D283C2212yes—
24C2×C4×D283C2211yescharacteristic, complemented
25Dic283⋊C4C2212yescomplemented
26Dic283⋊C4C2212yescomplemented
27C22⋊Dic283C2211yescharacteristic
28(C2×D283)⋊C4C2212yes—
29(C2×D283)⋊C4C2212yes—
30(C2×D283)⋊C4C2212yescomplemented
31C4×Dic283C2212yescomplemented
32C2×D4×C283C2211yescharacteristic
33C22×C4×C283C2211yescharacteristic
34C4⋊C4×C283C2212yescomplemented
35C22⋊C4×C283C2211yescharacteristic
36C22⋊C4×C283C2212yescomplemented
37C22×D283—22no—
38C22×D283—24no—
39C22×D283C2311yescharacteristic
40C22×D283C2312yes—
41Dic566—22no—
42D1132—24no—
43C22⋊D283—22no—
44C22⋊D283—24no—
45C22⋊D283—22no—
46C2×Dic283—22no—
47C2×Dic283D414yescomplemented
48C2×Dic283C2312yes—
49C2×Dic283C2311yescharacteristic
50C2×Dic283C2311yescharacteristic
51C2×Dic283C2311yescharacteristic
52C4×D283—24no—
53C4×D283—24no—
54C4×D283—22no—
55C23×C283C2311yescharacteristic
56C23×C283C2311yescharacteristic
57D4×C283—22no—
58C2×C4×C283—22no—
59C2×C4×C283C2312yes—
60C2×C4×C283C2312yes—
61C2×C4×C283C2311yescharacteristic
62C22×C283—22no—
63C22×C283—21no—
64C22×C283—22no—
65C22×C283C2×D412yes—
66C22×C283C2411yescharacteristic
67C2×D283—28no—
68C2×D283—22no—
69C2×D283—22no—
70C2×D283—21no—
71C2×D283—22no—
72C2×D283#4114yescomplemented
73C4×C283—22no—
74C4×C283—21no—
75C4×C283—22no—
76Dic283—21no—
77Dic283—22no—
78Dic283C2×D412yes—
79Dic283C2×D412yes—
80C2×C283—22no—
81C2×C283—41no—
82C2×C283C22×D411yescharacteristic
83C2×C283C2×#4112yes—
84D283—24no—
85D283—41no—
86C283#52511yescharacteristic, complemented, Sylow
87#525—2831nomaximal, Sylow
88C2×#41—2831no—
89C23×C4—2831no—
90#123—2831no—
91#123D28311yescharacteristic, complemented
92C22⋊Q8—2832no—
93#121—2832no—
94#120—2831no—
95#120—2831no—
96C4×D4—2832no—
97C4×D4—2832no—
98#117—2831no—
99C24—2831no—
100#41—5664no—
101C2×Q8—2831no—
102C2×D4—2832no—
103C2×D4—2831no—
104C2×D4—2831no—
105C2×D4—2832no—
106C2×D4C2×D28311yescharacteristic
107C22×C4—2831no—
108C22×C4—2831no—
109C22×C4—2832no—
110C22×C4—2832no—
111C22×C4—2831no—
112C22×C4—5664no—
113C22×C4C2×D28311yescharacteristic
114C4⋊C4—2832no—
115C4⋊C4—2832no—
116C4⋊C4C2×D28312yescomplemented
117C22⋊C4—2831no—
118C22⋊C4—2832no—
119C22⋊C4—2832no—
120C22⋊C4—2832no—
121C22⋊C4C2×D28311yescharacteristic
122C22⋊C4C2×D28312yescomplemented
123C42—2832no—
124C23—2832no—
125C23—2831no—
126C23—5664no—
127C23—5662no—
128C23C22×D28311yescharacteristic
129C23C22×D28311yescharacteristic
130Q8—5662no—
131D4—22no—
132D4—5664no—
133D4—5662no—
134D4—5664no—
135D4—5662no—
136C2×C4—22no—
137C2×C4—2834no—
138C2×C4—2831no—
139C2×C4—2831no—
140C2×C4—2832no—
141C2×C4—2831no—
142C2×C4—5664no—
143C2×C4—5664no—
144C2×C4—5662no—
145C2×C4—5662no—
146C2×C4C22×D28312yes—
147C2×C4C22×D28311yescharacteristic
148C2×C4C22×D28312yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—2834no—
153C22—5668no—
154C22—5662no—
155C22—5662no—
156C22—5661no—
157C22—5662no—
158C22D4×D28312yes—
159C22C23×D28311yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—2832no—
164C4—2832no—
165C4—5661no—
166C4—5662no—
167C2—22no—
168C2—41no—
169C2—5664no—
170C2—11321no—
171C2C2×D4×D28311yescharacteristic
172C2#41×D28312yes—
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
Fitting#123×C283C2
hypercenter#123D283
hypocenterC283#525
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#17985391C2semidirect
2. C22×C4×D283C2semidirect
3. #22583593C2semidirect
4. #22583588C2semidirect
5. #22583583C2semidirect
6. #22583580C2semidirect
7. #22583578C2semidirect
8. #22583572C2semidirect
9. (C22⋊D283)⋊C4C2semidirect
10. #22583566C2semidirect
11. #123×C283C2semidirect
14. C2×Dic566C22semidirect
18. C2×C22⋊D283C22semidirect
20. C22×Dic283C22semidirect
24. C2×C4×D283C22semidirect
25. Dic283⋊C4C22semidirect
26. Dic283⋊C4C22semidirect
30. (C2×D283)⋊C4C22semidirect
31. C4×Dic283C22semidirect
34. C4⋊C4×C283C22semidirect
36. C22⋊C4×C283C22semidirect
47. C2×Dic283D4semidirect
72. C2×D283#41semidirect
86. C283#525semidirect
91. #123D283semidirect
116. C4⋊C4C2×D283semidirect
122. C22⋊C4C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#179853912
C22×C4×D2832
#225835932
#225835882
#225835832
#225835802
#225835782
#225835722
(C22⋊D283)⋊C42
#225835662
#123×C2832
#525283