Finite Group Databasebeta

← #31823971

Subgroups — #31823971

Order 17984.

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×#17985137C211yesmaximal, characteristic, complemented
2C22×C4×D281C211yesmaximal, characteristic, complemented
3#22582862C211yesmaximal, characteristic, complemented
4#22582857C212yesmaximal, complemented
5#22582852C212yesmaximal, complemented
6#22582849C211yesmaximal, characteristic, complemented
7#22582847C211yesmaximal, characteristic, complemented
8#22582841C212yesmaximal, complemented
9#22582839C212yesmaximal, complemented
10#22582835C211yesmaximal, characteristic, complemented
11#123×C281C211yesmaximal, characteristic, complemented
12C23×D281C2211yescharacteristic
13#17985137—24no—
14C2×Dic562C2211yescharacteristic, complemented
15C2×D1124C2212yes—
16C2×C22⋊D281C2212yes—
17C2×C22⋊D281C2211yescharacteristic
18C2×C22⋊D281C2211yescharacteristic, complemented
19C22×Dic281C2211yescharacteristic
20C22×Dic281C2211yescharacteristic, complemented
21C2×C4×D281—24no—
22C2×C4×D281C2212yes—
23C2×C4×D281C2212yes—
24C2×C4×D281C2211yescharacteristic, complemented
25#17985117C2212yescomplemented
26#17985117C2212yescomplemented
27C22⋊Dic281C2211yescharacteristic
28#17985115C2212yes—
29#17985115C2212yes—
30#17985115C2212yescomplemented
31C4×Dic281C2212yescomplemented
32C2×D4×C281C2211yescharacteristic
33C22×C4×C281C2211yescharacteristic
34C4⋊C4×C281C2212yescomplemented
35C22⋊C4×C281C2211yescharacteristic
36C22⋊C4×C281C2212yescomplemented
37C22×D281—22no—
38C22×D281—24no—
39C22×D281C2311yescharacteristic
40C22×D281C2312yes—
41Dic562—22no—
42D1124—24no—
43C22⋊D281—22no—
44C22⋊D281—24no—
45C22⋊D281—22no—
46C2×Dic281—22no—
47C2×Dic281D414yescomplemented
48C2×Dic281C2312yes—
49C2×Dic281C2311yescharacteristic
50C2×Dic281C2311yescharacteristic
51C2×Dic281C2311yescharacteristic
52C4×D281—24no—
53C4×D281—24no—
54C4×D281—22no—
55C23×C281C2311yescharacteristic
56C23×C281C2311yescharacteristic
57D4×C281—22no—
58C2×C4×C281—22no—
59C2×C4×C281C2312yes—
60C2×C4×C281C2312yes—
61C2×C4×C281C2311yescharacteristic
62C22×C281—22no—
63C22×C281—21no—
64C22×C281—22no—
65C22×C281C2×D412yes—
66C22×C281C2411yescharacteristic
67C2×D281—28no—
68C2×D281—22no—
69C2×D281—22no—
70C2×D281—21no—
71C2×D281—22no—
72C2×D281#4114yescomplemented
73C4×C281—22no—
74C4×C281—21no—
75C4×C281—22no—
76Dic281—21no—
77Dic281—22no—
78Dic281C2×D412yes—
79Dic281C2×D412yes—
80C2×C281—22no—
81C2×C281—41no—
82C2×C281C22×D411yescharacteristic
83C2×C281C2×#4112yes—
84D281—24no—
85D281—41no—
86C281#52511yescharacteristic, complemented, Sylow
87#525—2811nomaximal, Sylow
88C2×#41—2811no—
89C23×C4—2811no—
90#123—2811no—
91#123D28111yescharacteristic, complemented
92C22⋊Q8—2812no—
93#121—2812no—
94#120—2811no—
95#120—2811no—
96C4×D4—2812no—
97C4×D4—2812no—
98#117—2811no—
99C24—2811no—
100#41—5624no—
101C2×Q8—2811no—
102C2×D4—2812no—
103C2×D4—2811no—
104C2×D4—2811no—
105C2×D4—2812no—
106C2×D4C2×D28111yescharacteristic
107C22×C4—2811no—
108C22×C4—2811no—
109C22×C4—2812no—
110C22×C4—2812no—
111C22×C4—2811no—
112C22×C4—5624no—
113C22×C4C2×D28111yescharacteristic
114C4⋊C4—2812no—
115C4⋊C4—2812no—
116C4⋊C4C2×D28112yescomplemented
117C22⋊C4—2811no—
118C22⋊C4—2812no—
119C22⋊C4—2812no—
120C22⋊C4—2812no—
121C22⋊C4C2×D28111yescharacteristic
122C22⋊C4C2×D28112yescomplemented
123C42—2812no—
124C23—2812no—
125C23—2811no—
126C23—5624no—
127C23—5622no—
128C23C22×D28111yescharacteristic
129C23C22×D28111yescharacteristic
130Q8—5622no—
131D4—22no—
132D4—5624no—
133D4—5622no—
134D4—5624no—
135D4—5622no—
136C2×C4—22no—
137C2×C4—2814no—
138C2×C4—2811no—
139C2×C4—2811no—
140C2×C4—2812no—
141C2×C4—2811no—
142C2×C4—5624no—
143C2×C4—5624no—
144C2×C4—5622no—
145C2×C4—5622no—
146C2×C4C22×D28112yes—
147C2×C4C22×D28111yescharacteristic
148C2×C4C22×D28112yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—2814no—
153C22—5628no—
154C22—5622no—
155C22—5622no—
156C22—5621no—
157C22—5622no—
158C22D4×D28112yes—
159C22C23×D28111yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—2812no—
164C4—2812no—
165C4—5621no—
166C4—5622no—
167C2—22no—
168C2—41no—
169C2—5624no—
170C2—11241no—
171C2C2×D4×D28111yescharacteristic
172C2#41×D28112yes—
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
Fitting#123×C281C2
hypercenter#123D281
hypocenterC281#525
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#17985137C2semidirect
2. C22×C4×D281C2semidirect
3. #22582862C2semidirect
4. #22582857C2semidirect
5. #22582852C2semidirect
6. #22582849C2semidirect
7. #22582847C2semidirect
8. #22582841C2semidirect
9. #22582839C2semidirect
10. #22582835C2semidirect
11. #123×C281C2semidirect
14. C2×Dic562C22semidirect
18. C2×C22⋊D281C22semidirect
20. C22×Dic281C22semidirect
24. C2×C4×D281C22semidirect
25. #17985117C22semidirect
26. #17985117C22semidirect
30. #17985115C22semidirect
31. C4×Dic281C22semidirect
34. C4⋊C4×C281C22semidirect
36. C22⋊C4×C281C22semidirect
47. C2×Dic281D4semidirect
72. C2×D281#41semidirect
86. C281#525semidirect
91. #123D281semidirect
116. C4⋊C4C2×D281semidirect
122. C22⋊C4C2×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#179851372
C22×C4×D2812
#225828622
#225828572
#225828522
#225828492
#225828472
#225828412
#225828392
#225828352
#123×C2812
#525281