Finite Group Databasebeta

← #31824029

Subgroups — #31824029

Order 17984.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×#17985138C211yesmaximal, characteristic, complemented
2C2×D4×D281C211yesmaximal, characteristic, complemented
3#22582875C212yesmaximal, complemented
4#22582865C212yesmaximal, complemented
5#22582854C211yesmaximal, characteristic, complemented
6#22582853C211yesmaximal, characteristic, complemented
7#22582850C211yesmaximal, characteristic, complemented
8#22582849C212yesmaximal, complemented
9#22582847C212yesmaximal, complemented
10#22582837C211yesmaximal, characteristic, complemented
11#121×C281C211yesmaximal, characteristic, complemented
12C23×D281C2212yes—
13#17985138—24no—
14C2×Dic562C2211yescharacteristic, complemented
15C2×D1124C2211yescharacteristic
16C2×D1124C2211yescharacteristic
17C2×D1124C2212yescomplemented
18C2×C22⋊D281C2211yescharacteristic
19C2×C22⋊D281C2212yes—
20C2×C22⋊D281C2211yescharacteristic, complemented
21C2×C22⋊D281C2212yescomplemented
22C2×C22⋊D281C2212yescomplemented
23D4×D281—24no—
24C2×C4×D281C2211yescharacteristic
25C2×C4×D281C2211yescharacteristic, complemented
26C4⋊Dic281C2211yescharacteristic, complemented
27C22⋊Dic281C2212yescomplemented
28#17985115C2212yes—
29#17985115C2212yescomplemented
30#17985115C2212yescomplemented
31C4×Dic281C2212yescomplemented
32C2×D4×C281C2211yescharacteristic
33C2×D4×C281C2212yescomplemented
34C22×C4×C281C2211yescharacteristic, complemented
35C4⋊C4×C281C2211yescharacteristic, complemented
36C22⋊C4×C281C2212yescomplemented
37C22×D281—24no—
38C22×D281—42no—
39C22×D281—42no—
40C22×D281C2312yes—
41C22×D281C2311yescharacteristic
42C22×D281C2311yescharacteristic
43Dic562—22no—
44D1124—22no—
45D1124—22no—
46D1124—42no—
47C22⋊D281—22no—
48C22⋊D281—24no—
49C22⋊D281—22no—
50C22⋊D281—42no—
51C22⋊D281—42no—
52C2×Dic281C2312yes—
53C2×Dic281C2311yescharacteristic
54C2×Dic281C2311yescharacteristic
55C4×D281—22no—
56C4×D281D414yescomplemented
57C23×C281C2312yes—
58C23×C281C2311yescharacteristic
59D4×C281—22no—
60D4×C281—42no—
61C2×C4×C281—22no—
62C2×C4×C281C2311yescharacteristic
63C2×C4×C281C2312yes—
64C2×C4×C281C2311yescharacteristic
65C22×C281—21no—
66C22×C281—22no—
67C22×C281—21no—
68C22×C281—22no—
69C22×C281—21no—
70C22×C281—22no—
71C22×C281C2411yescharacteristic
72C2×D281—21no—
73C2×D281—21no—
74C2×D281—21no—
75C2×D281—22no—
76C2×D281—21no—
77C2×D281—22no—
78C2×D281—21no—
79C2×D281—22no—
80C2×D281—48no—
81C2×D281C2×D412yes—
82C4×C281—21no—
83C4×C281—22no—
84C4×C281C2×D412yes—
85Dic281—21no—
86Dic281—22no—
87Dic281C2×D412yes—
88C2×C281—42no—
89C2×C281—41no—
90C2×C281C22×D411yescharacteristic
91C2×C281H(5,𝔽2)11yescharacteristic
92C2×C281H(5,𝔽2)11yescharacteristic
93D281—22no—
94D281—41no—
95D281—42no—
96C281#53511yescharacteristic, complemented, Sylow
97#535—2811nomaximal, Sylow
98C2×#41—2811no—
99C22×D4—2811no—
100#127—2812no—
101#124—2812no—
102#121—2811no—
103#121—2811no—
104#121—2811no—
105#121D28111yescharacteristic, complemented
106#120—2812no—
107#120—2812no—
108#117—2811no—
109C24—2812no—
110#41—5624no—
111C2×Q8—2811no—
112C2×D4—2811no—
113C2×D4—2812no—
114C2×D4—2811no—
115C2×D4—2812no—
116C2×D4—2812no—
117C2×D4—2811no—
118C2×D4—2811no—
119C2×D4—2812no—
120C2×D4—5624no—
121C2×D4C2×D28111yescharacteristic
122C2×D4C2×D28112yescomplemented
123C22×C4—2811no—
124C22×C4—2811no—
125C22×C4C2×D28111yescharacteristic, complemented
126C4⋊C4—2811no—
127C4⋊C4C2×D28111yescharacteristic, complemented
128C22⋊C4—2812no—
129C22⋊C4—2812no—
130C22⋊C4—2812no—
131C22⋊C4—2812no—
132C22⋊C4C2×D28112yescomplemented
133C42—2812no—
134C23—2811no—
135C23—2812no—
136C23—2811no—
137C23—5624no—
138C23—11242no—
139C23—11242no—
140C23C22×D28112yes—
141C23C22×D28111yescharacteristic
142Q8—5622no—
143D4—22no—
144D4—42no—
145D4—5622no—
146D4—5624no—
147D4—5622no—
148D4—5622no—
149D4—5622no—
150D4—11242no—
151D4—11242no—
152D4—11242no—
153C2×C4—22no—
154C2×C4—2811no—
155C2×C4—2814no—
156C2×C4—2812no—
157C2×C4—2811no—
158C2×C4—5622no—
159C2×C4C22×D28112yes—
160C2×C4C22×D28111yescharacteristic
161C2×C4C22×D28111yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—2812no—
169C22—5621no—
170C22—5621no—
171C22—5621no—
172C22—5622no—
173C22—5621no—
174C22—5622no—
175C22—5621no—
176C22—5622no—
177C22—11248no—
178C22C23×D28111yescharacteristic
179C4—21no—
180C4—22no—
181C4—2812no—
182C4—5621no—
183C4—5622no—
184C4D4×D28112yes—
185C2—42no—
186C2—41no—
187C2—5622no—
188C2—11242no—
189C2—11241no—
190C2C2×D4×D28111yescharacteristic
191C2#2258292411yescharacteristic
192C2#2258292511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D281
commutator, socle, cosocleC22×C281C24
Fitting#121×C281C2
hypercenter#121D281
hypocenterC281#535
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#17985138C2semidirect
2. C2×D4×D281C2semidirect
3. #22582875C2semidirect
4. #22582865C2semidirect
5. #22582854C2semidirect
6. #22582853C2semidirect
7. #22582850C2semidirect
8. #22582849C2semidirect
9. #22582847C2semidirect
10. #22582837C2semidirect
11. #121×C281C2semidirect
14. C2×Dic562C22semidirect
17. C2×D1124C22semidirect
20. C2×C22⋊D281C22semidirect
21. C2×C22⋊D281C22semidirect
22. C2×C22⋊D281C22semidirect
25. C2×C4×D281C22semidirect
26. C4⋊Dic281C22semidirect
27. C22⋊Dic281C22semidirect
29. #17985115C22semidirect
30. #17985115C22semidirect
31. C4×Dic281C22semidirect
33. C2×D4×C281C22semidirect
34. C22×C4×C281C22semidirect
35. C4⋊C4×C281C22semidirect
36. C22⋊C4×C281C22semidirect
56. C4×D281D4semidirect
96. C281#535semidirect
105. #121D281semidirect
122. C2×D4C2×D281semidirect
125. C22×C4C2×D281semidirect
127. C4⋊C4C2×D281semidirect
132. C22⋊C4C2×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#179851382
C2×D4×D2812
#225828752
#225828652
#225828542
#225828532
#225828502
#225828492
#225828472
#225828372
#121×C2812
#535281