Finite Group Databasebeta

← #31823973

Subgroups — #31823973

Order 17984.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 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
1C2×#17985137C211yesmaximal, characteristic, complemented
2C22×C4×D281C211yesmaximal, characteristic, complemented
3#22582861C212yesmaximal, complemented
4#22582859C211yesmaximal, characteristic, complemented
5#22582858C211yesmaximal, characteristic, complemented
6#22582850C211yesmaximal, characteristic, complemented
7#22582847C212yesmaximal, complemented
8D4×Dic281C212yesmaximal, complemented
9#22582839C212yesmaximal, complemented
10#22582837C211yesmaximal, characteristic, complemented
11#121×C281C211yesmaximal, characteristic, complemented
12C23×D281C2211yescharacteristic
13#17985137—24no—
14C2×Dic562C2211yescharacteristic, complemented
15C2×C22⋊D281C2212yes—
16C2×C22⋊D281C2212yes—
17C22×Dic281C2211yescharacteristic
18C22×Dic281C2212yescomplemented
19C2×C4×D281—24no—
20C2×C4×D281C2211yescharacteristic
21C2×C4×D281C2211yescharacteristic
22C2×C4×D281C2211yescharacteristic
23C2×C4×D281C2211yescharacteristic
24C4⋊Dic281C2211yescharacteristic, complemented
25C4⋊Dic281C2212yescomplemented
26#17985117C2212yescomplemented
27C22⋊Dic281C2212yes—
28C22⋊Dic281C2212yescomplemented
29#17985115C2212yes—
30#17985115C2212yes—
31C4×Dic281C2212yescomplemented
32C2×D4×C281C2212yes—
33C2×D4×C281C2211yescharacteristic, complemented
34C22×C4×C281C2211yescharacteristic
35C4⋊C4×C281C2211yescharacteristic, complemented
36C22⋊C4×C281C2212yescomplemented
37C22×D281—22no—
38C22×D281—22no—
39C22×D281—22no—
40C22×D281C2311yescharacteristic
41C22×D281C2311yescharacteristic
42Dic562—22no—
43C22⋊D281—24no—
44C22⋊D281—24no—
45C2×Dic281—22no—
46C2×Dic281—24no—
47C2×Dic281C2312yes—
48C2×Dic281C2312yes—
49C2×Dic281C2311yescharacteristic
50C2×Dic281C2311yescharacteristic
51C4×D281—22no—
52C4×D281—22no—
53C4×D281—22no—
54C4×D281D414yescomplemented
55C23×C281C2312yes—
56C23×C281C2311yescharacteristic
57D4×C281—24no—
58D4×C281—22no—
59C2×C4×C281—22no—
60C2×C4×C281C2311yescharacteristic
61C2×C4×C281C2312yes—
62C2×C4×C281C2311yescharacteristic
63C22×C281—21no—
64C22×C281—21no—
65C22×C281—22no—
66C22×C281—22no—
67C22×C281—22no—
68C22×C281#4112yescomplemented
69C22×C281C2411yescharacteristic
70C2×D281—28no—
71C2×D281—21no—
72C2×D281—21no—
73C2×D281—21no—
74C2×D281—21no—
75C2×D281C2×D412yes—
76C2×D281#4112yescomplemented
77C4×C281—21no—
78C4×C281—22no—
79C4×C281C2×D412yes—
80Dic281—21no—
81Dic281—22no—
82Dic281—22no—
83Dic281C2×D412yes—
84C2×C281—22no—
85C2×C281—42no—
86C2×C281C22×D411yescharacteristic
87C2×C281C2×#4111yescharacteristic
88C2×C281C2×#4111yescharacteristic
89D281—22no—
90D281—22no—
91C281#52511yescharacteristic, complemented, Sylow
92#525—2811nomaximal, Sylow
93C2×#41—2811no—
94C23×C4—2811no—
95#123—2812no—
96C22⋊Q8—2811no—
97C22⋊Q8—2811no—
98#121—2811no—
99#121D28111yescharacteristic, complemented
100#120—2812no—
101C4×D4—2812no—
102C4×D4—2812no—
103#117—2811no—
104C24—2811no—
105#41—5624no—
106C2×Q8—2811no—
107C2×D4—2812no—
108C2×D4—2812no—
109C2×D4C2×D28112yes—
110C2×D4C2×D28111yescharacteristic, complemented
111C22×C4—2811no—
112C22×C4—2811no—
113C22×C4—2812no—
114C22×C4—2811no—
115C22×C4—2811no—
116C22×C4—2811no—
117C22×C4—5624no—
118C22×C4C2×D28111yescharacteristic
119C4⋊C4—2812no—
120C4⋊C4—2811no—
121C4⋊C4—2812no—
122C4⋊C4C2×D28111yescharacteristic, complemented
123C22⋊C4—2812no—
124C22⋊C4—2812no—
125C22⋊C4—2812no—
126C22⋊C4—2812no—
127C22⋊C4C2×D28112yescomplemented
128C42—2812no—
129C23—2811no—
130C23—2811no—
131C23—5622no—
132C23—5622no—
133C23—5622no—
134C23C22×D28112yes—
135C23C22×D28111yescharacteristic
136Q8—5622no—
137D4—24no—
138D4—22no—
139D4—5624no—
140D4—5624no—
141C2×C4—22no—
142C2×C4—2811no—
143C2×C4—2814no—
144C2×C4—2812no—
145C2×C4—2811no—
146C2×C4—2812no—
147C2×C4—5622no—
148C2×C4—5622no—
149C2×C4—5622no—
150C2×C4—5624no—
151C2×C4—5622no—
152C2×C4C22×D28112yes—
153C2×C4C22×D28111yescharacteristic
154C2×C4C22×D28111yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—2812no—
161C22—2812no—
162C22—5628no—
163C22—5621no—
164C22—5621no—
165C22—5621no—
166C22—5621no—
167C22#1798513712yescomplemented
168C22C23×D28111yescharacteristic
169C4—21no—
170C4—22no—
171C4—2812no—
172C4—5621no—
173C4—5622no—
174C4—5622no—
175C4D4×D28112yes—
176C2—22no—
177C2—42no—
178C2—5622no—
179C2—5622no—
180C2C2×D4×D28111yescharacteristic
181C2#41×D28111yescharacteristic
182C2C2×#1798513711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
Fitting#121×C281C2
hypercenter#121D281
hypocenterC281#525
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#17985137C2semidirect
2. C22×C4×D281C2semidirect
3. #22582861C2semidirect
4. #22582859C2semidirect
5. #22582858C2semidirect
6. #22582850C2semidirect
7. #22582847C2semidirect
8. D4×Dic281C2semidirect
9. #22582839C2semidirect
10. #22582837C2semidirect
11. #121×C281C2semidirect
14. C2×Dic562C22semidirect
18. C22×Dic281C22semidirect
24. C4⋊Dic281C22semidirect
25. C4⋊Dic281C22semidirect
26. #17985117C22semidirect
28. C22⋊Dic281C22semidirect
31. C4×Dic281C22semidirect
33. C2×D4×C281C22semidirect
35. C4⋊C4×C281C22semidirect
36. C22⋊C4×C281C22semidirect
54. C4×D281D4semidirect
68. C22×C281#41semidirect
76. C2×D281#41semidirect
91. C281#525semidirect
99. #121D281semidirect
110. C2×D4C2×D281semidirect
122. C4⋊C4C2×D281semidirect
127. C22⋊C4C2×D281semidirect
167. C22#17985137semidirect

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
#225828612
#225828592
#225828582
#225828502
#225828472
D4×Dic2812
#225828392
#225828372
#121×C2812
#525281